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Journal articles on the topic 'Finsler'

Author: Grafiati

Published: 4 June 2021

Last updated: 1 February 2022

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1

LI, JINTANG. "STABLE HARMONIC MAPS BETWEEN FINSLER MANIFOLDS AND SSU MANIFOLDS." Communications in Contemporary Mathematics 14, no. 03 (2012): 1250015. http://dx.doi.org/10.1142/s0219199712500150.

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Using the properties of Cartan tensor, we rewrite the second variation formula for harmonic maps between Finsler manifolds, and we prove that there is no non-degenerate stable harmonic map from a compact SSU manifold to any Finsler manifold, which is obtained by Howard and Wei for the Riemannian case. We also include a proof of a theorem of Shen–Wei which states that there is no non-degenerate stable harmonic map from a compact Finsler manifold to any SSU manifold, by the same second variational formula (see Eq. (2.1) in [Y. B. Shen and S. W. Wei, The stability of harmonic maps on Finster mani

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2

Mandal, Khageswar. "The Β-Change by Finsler Metric of C-Reducible Finsler Spaces in Finsler Geometry". Tribhuvan University Journal 33, № 1 (2019): 1–10. http://dx.doi.org/10.3126/tuj.v33i1.28674.

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This paper considered about the β-Change of Finsler metric L given by L*= f(L, β), where f is any positively homogeneous function of degree one in L and β and obtained the β-Change by Finsler metric of C-reducible Finsler spaces. Also further obtained the condition that a C-reducible Finsler space is transformed to a C-reducible Finsler space by a β-change of Finsler metric.

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3

Xia, Hongchuan, and Chunping Zhong. "On complex Berwald metrics which are not conformal changes of complex Minkowski metrics." Advances in Geometry 18, no. 3 (2018): 373–84. http://dx.doi.org/10.1515/advgeom-2017-0062.

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AbstractWe investigate a class of complex Finsler metrics on a domain D ⊂ ℂn. Necessary and sufficient conditions for these metrics to be strongly pseudoconvex complex Finsler metrics, or complex Berwald metrics, are given. The complex Berwald metrics constructed in this paper are neither trivial Hermitian metrics nor conformal changes of complex Minkowski metrics. We give a characterization of complex Berwald metrics which are of isotropic holomorphic curvatures, and also give characterizations of complex Finsler metrics of this class to be Kähler Finsler or weakly Kähler Finsler metrics. Mor

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4

Minas, Georgios, Emmanuel Saridakis, Panayiotis Stavrinos, and Alkiviadis Triantafyllopoulos. "Bounce Cosmology in Generalized Modified Gravities." Universe 5, no. 3 (2019): 74. http://dx.doi.org/10.3390/universe5030074.

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We investigate the bounce realization in the framework of generalized modified gravities arising from Finsler and Finsler-like geometries. In particular, a richer intrinsic geometrical structure is reflected in the appearance of extra degrees of freedom in the Friedmann equations that can drive the bounce. We examine various Finsler and Finsler-like constructions. In the cases of general very special relativity, as well as of Finsler-like gravity on the tangent bundle, we show that a bounce cannot easily be obtained. However, in the Finsler–Randers space, induced scalar anisotropy can fulfil b

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5

Yallappa Kumbar, Mallikarjun, Narasimhamurthy Senajji Kampalappa, Thippeswamy Komalobiah Rajanna та Kavyashree Ambale Rajegowda. "Killing Vector Fields in Generalized Conformalβ-Change of Finsler Spaces". Journal of Mathematics 2015 (2015): 1–5. http://dx.doi.org/10.1155/2015/456291.

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We consider a Finsler space equipped with a Generalized Conformalβ-change of metric and study the Killing vector fields that correspond between the original Finsler space and the Finsler space equipped with Generalized Conformalβ-change of metric. We obtain necessary and sufficient condition for a vector field Killing in the original Finsler space to be Killing in the Finsler space equipped with Generalized Conformalβ-change of metric.

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6

Hohmann, Manuel, Christian Pfeifer, and Nicoleta Voicu. "Cosmological Finsler Spacetimes." Universe 6, no. 5 (2020): 65. http://dx.doi.org/10.3390/universe6050065.

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Applying the cosmological principle to Finsler spacetimes, we identify the Lie Algebra of symmetry generators of spatially homogeneous and isotropic Finsler geometries, thus generalising Friedmann-Lemaître-Robertson-Walker geometry. In particular, we find the most general spatially homogeneous and isotropic Berwald spacetimes, which are Finsler spacetimes that can be regarded as closest to pseudo-Riemannian geometry. They are defined by a Finsler Lagrangian built from a zero-homogeneous function on the tangent bundle, which encodes the velocity dependence of the Finsler Lagrangian in a very sp

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7

VACARU, SERGIU I. "PRINCIPLES OF EINSTEIN–FINSLER GRAVITY AND PERSPECTIVES IN MODERN COSMOLOGY." International Journal of Modern Physics D 21, no. 09 (2012): 1250072. http://dx.doi.org/10.1142/s0218271812500721.

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We study the geometric and physical foundations of Finsler gravity theories with metric compatible connections defined on tangent bundles, or (pseudo) Riemannian manifolds, endowed with nonholonomic frame structure. Several generalizations and alternatives to Einstein gravity are considered, including modifications with broken local Lorentz invariance. It is also shown how such theories (and general relativity) can be equivalently re-formulated in Finsler like variables. We focus on prospects in modern cosmology and Finsler acceleration of Universe. Einstein–Finsler gravity theories are elabor

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8

Feng, Huitao, Kefeng Liu, and Xueyuan Wan. "Chern forms of holomorphic Finsler vector bundles and some applications." International Journal of Mathematics 27, no. 04 (2016): 1650030. http://dx.doi.org/10.1142/s0129167x16500300.

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In this paper, we present two kinds of total Chern forms [Formula: see text] and [Formula: see text] as well as a total Segre form [Formula: see text] of a holomorphic Finsler vector bundle [Formula: see text] expressed by the Finsler metric [Formula: see text], which answers a question of Faran [The equivalence problem for complex Finsler Hamiltonians, in Finsler Geometry, Contemporary Mathematics, Vol. 196 (American Mathematical Society, Providence, RI, 1996), pp. 133–144] to some extent. As some applications, we show that the signed Segre forms [Formula: see text] are positive [Formula: see

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9

Deng, Shaoqiang. "An Algebraic Approach to Weakly Symmetric Finsler Spaces." Canadian Journal of Mathematics 62, no. 1 (2010): 52–73. http://dx.doi.org/10.4153/cjm-2010-004-x.

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AbstractIn this paper, we introduce a new algebraic notion, weakly symmetric Lie algebras, to give an algebraic description of an interesting class of homogeneous Riemann-Finsler spaces, weakly symmetric Finsler spaces. Using this new definition, we are able to give a classification of weakly symmetric Finsler spaces with dimensions 2 and 3. Finally, we show that all the non-Riemannian reversible weakly symmetric Finsler spaces we find are non-Berwaldian and with vanishing S-curvature. Thismeans that reversible non-Berwaldian Finsler spaces with vanishing S-curvaturemay exist at large. Hence t

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10

Duval, C. "Finsler Spinoptics." Communications in Mathematical Physics 283, no. 3 (2008): 701–27. http://dx.doi.org/10.1007/s00220-008-0573-7.

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11

Bejancu, Aurel, and Tominosuke Otsuki. "General Finsler connections on a Finsler vector bundle." Kodai Mathematical Journal 10, no. 1 (1987): 143–52. http://dx.doi.org/10.2996/kmj/1138037369.

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12

Rutz, Solange F., and Renato Portugal. "FINSLER: A computer algebra package for Finsler geometries." Nonlinear Analysis: Theory, Methods & Applications 47, no. 9 (2001): 6121–34. http://dx.doi.org/10.1016/s0362-546x(01)00683-6.

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13

Liu, Huaifu, and Xiaohuan Mo. "Finsler Warped Product Metrics of Douglas Type." Canadian Mathematical Bulletin 62, no. 1 (2019): 119–30. http://dx.doi.org/10.4153/cmb-2017-077-0.

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AbstractIn this paper, we study the warped structures of Finsler metrics. We obtain the differential equation that characterizes Finsler warped product metrics with vanishing Douglas curvature. By solving this equation, we obtain all Finsler warped product Douglas metrics. Some new Douglas Finsler metrics of this type are produced by using known spherically symmetric Douglas metrics.

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14

PAPADOPOULOS, ATHANASE, and MARC TROYANOV. "Weak Finsler structures and the Funk weak metric." Mathematical Proceedings of the Cambridge Philosophical Society 147, no. 2 (2009): 419–37. http://dx.doi.org/10.1017/s0305004109002461.

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AbstractWe discuss general notions of metrics and of Finsler structures which we call weak metrics and weak Finsler structures. Any convex domain carries a canonical weak Finsler structure, which we call its tautological weak Finsler structure. We compute distances in the tautological weak Finsler structure of a domain and we show that these are given by the so-called Funk weak metric. We conclude the paper with a discussion of geodesics, of metric balls, of convexity, and of rigidity properties of the Funk weak metric.

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15

Zhu, Hongmei, and Haixia Zhang. "Projective Ricci flat spherically symmetric Finsler metrics." International Journal of Mathematics 29, no. 11 (2018): 1850078. http://dx.doi.org/10.1142/s0129167x18500787.

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In Finsler geometry, the projective Ricci curvature is an important projective invariant. In this paper, we characterize projective Ricci flat spherically symmetric Finsler metrics. Under a certain condition, we prove that a projective Ricci flat spherically symmetric Finsler metric must be a Douglas metric. Moreover, we construct a class of new nontrivial examples on projective Ricci flat Finsler metrics.

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16

Mo, Xiaohuan, and Zhongmin Shen. "On Negatively Curved Finsler Manifolds of Scalar Curvature." Canadian Mathematical Bulletin 48, no. 1 (2005): 112–20. http://dx.doi.org/10.4153/cmb-2005-010-3.

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AbstractIn this paper, we prove a global rigidity theorem for negatively curved Finsler metrics on a compact manifold of dimension n ≥ 3. We show that for such a Finsler manifold, if the flag curvature is a scalar function on the tangent bundle, then the Finsler metric is of Randers type. We also study the case when the Finsler metric is locally projectively flat.

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17

SHEN, YIBING, and WEI ZHAO. "SOME RESULTS ON FUNDAMENTAL GROUPS AND BETTI NUMBERS OF FINSLER MANIFOLDS." International Journal of Mathematics 23, no. 06 (2012): 1250063. http://dx.doi.org/10.1142/s0129167x12500632.

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In this paper the relationship between the Ricci curvature and the fundamental groups of Finsler manifolds are studied. We give an estimate of the first Betti number of a compact Finsler manifold. Two finiteness theorems for fundamental groups of compact Finsler manifolds are proved. Moreover, the growth of fundamental groups of Finsler manifolds with almost-nonnegative Ricci curvature are considered.

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18

MO, XIAOHUAN, and HONGMEI ZHU. "ON A CLASS OF PROJECTIVELY FLAT FINSLER METRICS OF NEGATIVE CONSTANT FLAG CURVATURE." International Journal of Mathematics 23, no. 08 (2012): 1250084. http://dx.doi.org/10.1142/s0129167x1250084x.

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In this paper, we prove a structure theorem for projectively flat Finsler metrics of negative constant flag curvature. We show that for such a Finsler metric if the orthogonal group acts as isometries, then the Finsler metric is a slight generalization of Chern–Shen's construction Riemann–Finsler geometry, Nankai Tracts in Mathematics, Vol. 6 (World Scientific Publishing, Hackensack, NJ, 2005), x+192 pp.

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19

Ionescu, Alexandru, and Gheorghe Munteanu. "The warped product of holomorphic Lie algebroids." Analele Universitatii "Ovidius" Constanta - Seria Matematica 28, no. 1 (2020): 117–34. http://dx.doi.org/10.2478/auom-2020-0009.

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AbstractWe introduce the warped product of two holomorphic Finsler algebroids and we define a complex Finsler function on it. We study the Chern-Finsler connections of the bundles and of their product and we investigate their curvatures. We use the geometrical setting of the prolongations of the two bundles to obtain some similar and some different properties from the ones of the warped product of Finsler manifolds.

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20

He, Qun, and Daxiao Zheng. "Some rigidity theorems of harmonic maps between Finsler manifolds." International Journal of Mathematics 25, no. 05 (2014): 1450043. http://dx.doi.org/10.1142/s0129167x14500438.

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This paper is to study further properties of harmonic maps between Finsler manifolds. It is proved that any conformal harmonic map from an n(>2)-dimensional Finsler manifold to a Finsler manifold must be homothetic and some rigidity theorems for harmonic maps between Finsler manifolds are given, which improve some results in earlier papers and generalize Eells–Sampson's theorem and Sealey's theorem in Riemannian Geometry.

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21

Kushwaha, Ramdayal Singh, та Gauree Shanker. "On the ℒ-duality of a Finsler space with exponential metric αeβ/α". Acta Universitatis Sapientiae, Mathematica 10, № 1 (2018): 167–77. http://dx.doi.org/10.2478/ausm-2018-0014.

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Abstract The (α, β)-metrics are the most studied Finsler metrics in Finsler geometry with Randers, Kropina and Matsumoto metrics being the most explored metrics in modern Finsler geometry. The ℒ-dual of Randers, Kropina and Matsumoto space have been introduced in [3, 4, 5], also in recent the ℒ-dual of a Finsler space with special (α, β)-metric and generalized Matsumoto spaces have been introduced in [16, 17]. In this paper, we find the ℒ-dual of a Finsler space with an exponential metric αeβ/α, where α is Riemannian metric and β is a non-zero one form.

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22

Peyghan, E., A. Tayebi, and L. Nourmohammadi Far. "On Twisted Products Finsler Manifolds." ISRN Geometry 2013 (July 10, 2013): 1–12. http://dx.doi.org/10.1155/2013/732432.

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On the product of two Finsler manifolds , we consider the twisted metric which is constructed by using Finsler metrics and on the manifolds and , respectively. We introduce horizontal and vertical distributions on twisted product Finsler manifold and study C-reducible and semi-C-reducible properties of this manifold. Then we obtain the Riemannian curvature and some of non-Riemannian curvatures of the twisted product Finsler manifold such as Berwald curvature, mean Berwald curvature, and we find the relations between these objects and their corresponding objects on and . Finally, we study local

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23

Peyghan, Esmaeil, and Esa Sharahi. "Vector Bundles and Paracontact Finsler Structures." Facta Universitatis, Series: Mathematics and Informatics 33, no. 2 (2018): 231. http://dx.doi.org/10.22190/fumi1802231p.

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Almost paracontact and normal almost paracontact Finsler structures on a vector bundle are defined. Finding some conditions, integrability of these structures are studied. Moreover, we define paracontact metric, para- Sasakian and K-paracontact Finsler structures and study some properties of these structures. For a K-paracontact Finsler structure, we find the vertical and horizontal flag curvatures. Then, defining vertical φ-flag curvature, we prove that every locally symmetric para-Sasakian Finsler structure has negative vertical φ-flag curvature. Finally, we define the horizontal and vertica

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24

Tabatabaeifar, Tayebeh, Behzad Najafi, and Mehdi Rafie-Rad. "On almost contact Finsler structures." International Journal of Geometric Methods in Modern Physics 17, no. 08 (2020): 2050126. http://dx.doi.org/10.1142/s0219887820501261.

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We introduce almost contact and cosymplectic Finsler manifolds. Then, we characterize almost contact Randers metrics. It is proved that a cosymplectic Finsler manifold of constant flag curvature must have vanishing flag curvature. We prove that every cosymplectic Finsler manifold is a Landsberg space, under a mild condition. Finally, we show that a cosymplectic Finsler manifold is a Douglas space if and only if it is a Berwald space.

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25

Tiwari, Bankteshwar, and Manoj Kumar. "On Randers change of a Finsler space with mth-root metric." International Journal of Geometric Methods in Modern Physics 11, no. 10 (2014): 1450087. http://dx.doi.org/10.1142/s021988781450087x.

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In this paper, we find a condition under which a Finsler space with Randers change of mth-root metric is projectively related to a mth-root metric and also we find a condition under which this Randers transformed mth-root Finsler metric is locally dually flat. Moreover, if transformed Finsler metric is conformal to the mth-root Finsler metric, then we prove that both of them reduce to Riemannian metrics.

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26

XIAO, JINXIU, CHUNHUI QIU, QUN HE, and ZHIHUA CHEN. "LAPLACIAN COMPARISON ON COMPLEX FINSLER MANIFOLDS AND ITS APPLICATIONS." International Journal of Mathematics 24, no. 05 (2013): 1350034. http://dx.doi.org/10.1142/s0129167x13500341.

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By defining the Rund Laplacian, we obtain the first and the second holomorphic variation formulas for the strongly pseudoconvex complex Finsler metric. Using the holomorphic variation formulas, we get an estimate for the Levi forms of distance function on complex Finsler manifolds. Further, an estimate for the Rund Laplacians of distance function on strongly pseudoconvex complex Finsler manifolds is obtained. As its applications, we get the Bonnet theorem and maximum principle on complex Finsler manifolds.

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27

Ida, Cristian. "Vertical Chern Type Classes on Complex Finsler Bundles." Annals of the Alexandru Ioan Cuza University - Mathematics 57, no. 2 (2011): 377–86. http://dx.doi.org/10.2478/v10157-011-0033-0.

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Vertical Chern Type Classes on Complex Finsler BundlesIn the present paper, we define vertical Chern type classes on complex Finsler bundles, as an extension of thev-cohomology groups theory on complex Finsler manifolds. These classes are introduced in a classical way by using closed differential forms with respect to the conjugated vertical differential in terms of the vertical curvature form of Chern-Finsler linear connection. Also, some invariance properties of these classes are studied.

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28

Wei, Shihshu Walter, and Bing Ye Wu. "Generalized Hardy Type and Caffarelli–Kohn–Nirenberg Type Inequalities on Finsler Manifolds." International Journal of Mathematics 31, no. 13 (2020): 2050109. http://dx.doi.org/10.1142/s0129167x20501098.

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In this paper we derive both local and global geometric inequalities on general Riemannnian and Finsler manifolds and prove generalized Caffarelli–Kohn–Nirenberg type and Hardy type inequalities on Finsler manifolds, illuminating curvatures of both Riemannian and Finsler manifolds influence geometric inequalities.

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29

Zhao, Wei, and Yibing Shen. "A Universal Volume Comparison Theorem for Finsler Manifolds and Related Results." Canadian Journal of Mathematics 65, no. 6 (2013): 1401–35. http://dx.doi.org/10.4153/cjm-2012-053-4.

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AbstractIn this paper, we establish a universal volume comparison theorem for Finsler manifolds and give the Berger–Kazdan inequality and Santalá's formula in Finsler geometry. Based on these, we derive a Berger–Kazdan type comparison theorem and a Croke type isoperimetric inequality for Finsler manifolds.

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30

Xu, Ming, and Shaoqiang Deng. "Homogeneous Finsler spaces and the flag-wise positively curved condition." Forum Mathematicum 30, no. 6 (2018): 1521–37. http://dx.doi.org/10.1515/forum-2018-0130.

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Abstract In this paper, we introduce the flag-wise positively curved condition for Finsler spaces (the (FP) condition), which means that in each tangent plane, there exists a flag pole in this plane such that the corresponding flag has positive flag curvature. Applying the Killing navigation technique, we find a list of compact coset spaces admitting non-negatively curved homogeneous Finsler metrics satisfying the (FP) condition. Using a crucial technique we developed previously, we prove that most of these coset spaces cannot be endowed with positively curved homogeneous Finsler metrics. We a

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31

DENG, SHAOQIANG, and ZIXIN HOU. "WEAKLY SYMMETRIC FINSLER SPACES." Communications in Contemporary Mathematics 12, no. 02 (2010): 309–23. http://dx.doi.org/10.1142/s0219199710003816.

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In this paper, we introduce the notion of weakly symmetric Finsler spaces and study some geometrical properties of such spaces. In particular, we prove that each maximal geodesic in a weakly symmetric Finsler space is the orbit of a one-parameter subgroup of the full isometric group. This implies that each weakly symmetric Finsler space has vanishing S-curvature. As an application of these results, we prove that there exist reversible non-Berwaldian Finsler metrics on the 3-dimensional sphere with vanishing S-curvature. This solves an open problem raised by Z. Shen.

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32

Shanker, Gauree, and Sarita Rani. "On S-curvature of a homogeneous Finsler space with square metric." International Journal of Geometric Methods in Modern Physics 17, no. 02 (2020): 2050019. http://dx.doi.org/10.1142/s021988782050019x.

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The study of curvature properties of homogeneous Finsler spaces with [Formula: see text]-metrics is one of the central problems in Riemann–Finsler geometry. In this paper, the existence of invariant vector fields on a homogeneous Finsler space with square metric is proved. Further, an explicit formula for [Formula: see text]-curvature of a homogeneous Finsler space with square metric is established. Finally, using the formula of [Formula: see text]-curvature, the mean Berwald curvature of aforesaid [Formula: see text]-metric is calculated.

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33

VACARU, SERGIU I. "METRIC COMPATIBLE OR NON-COMPATIBLE FINSLER–RICCI FLOWS." International Journal of Geometric Methods in Modern Physics 09, no. 05 (2012): 1250041. http://dx.doi.org/10.1142/s0219887812500417.

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There were elaborated different models of Finsler geometry using the Cartan (metric compatible), or Berwald and Chern (metric non-compatible) connections, the Ricci flag curvature, etc. In a series of works, we studied (non)-commutative metric compatible Finsler and non-holonomic generalizations of the Ricci flow theory [see S. Vacaru, J. Math. Phys. 49 (2008) 043504; 50 (2009) 073503 and references therein]. The aim of this work is to prove that there are some models of Finsler gravity and geometric evolution theories with generalized Perelman's functionals, and correspondingly derived non-ho

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34

YOUSSEF, NABIL L., S. H. ABED та S. G. ELGENDI. "GENERALIZED β-CONFORMAL CHANGE OF FINSLER METRICS". International Journal of Geometric Methods in Modern Physics 07, № 04 (2010): 565–82. http://dx.doi.org/10.1142/s0219887810004440.

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In this paper, we introduce and investigate a general transformation or change of Finsler metrics, which is referred to as a generalized β-conformal change: [Formula: see text] This transformation combines both β-change and conformal change in a general setting. The change, under this transformation, of the fundamental Finsler connections, together with their associated geometric objects, are obtained. Some invariants and various special Finsler spaces are investigated under this change. The most important changes of Finsler metrics existing in the literature are deduced from the generalized β

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35

Fuster, Andrea, Sjors Heefer, Christian Pfeifer, and Nicoleta Voicu. "On the Non Metrizability of Berwald Finsler Spacetimes." Universe 6, no. 5 (2020): 64. http://dx.doi.org/10.3390/universe6050064.

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We investigate whether Szabo’s metrizability theorem can be extended to Finsler spaces of indefinite signature. For smooth, positive definite Finsler metrics, this important theorem states that, if the metric is of Berwald type (i.e., its Chern–Rund connection defines an affine connection on the underlying manifold), then it is affinely equivalent to a Riemann space, meaning that its affine connection is the Levi–Civita connection of some Riemannian metric. We show for the first time that this result does not extend to general Finsler spacetimes. More precisely, we find a large class of Berwal

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36

Shanker, Gauree, and Kirandeep Kaur. "Homogeneous Finsler spaces with exponential metric." Advances in Geometry 20, no. 3 (2020): 391–400. http://dx.doi.org/10.1515/advgeom-2020-0008.

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AbstractWe prove the existence of an invariant vector field on a homogeneous Finsler space with exponential metric, and we derive an explicit formula for the S-curvature of a homogeneous Finsler space with exponential metric. Using this formula, we obtain a formula for the mean Berwald curvature of such a homogeneous Finsler space.

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37

Garrido, M. I., J. A. Jaramillo, and Y. C. Rangel. "Smooth Approximation of Lipschitz Functions on Finsler Manifolds." Journal of Function Spaces and Applications 2013 (2013): 1–10. http://dx.doi.org/10.1155/2013/164571.

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We study the smooth approximation of Lipschitz functions on Finsler manifolds, keeping control on the corresponding Lipschitz constants. We prove that, given a Lipschitz functionf:M→ℝdefined on a connected, second countable Finsler manifoldM, for each positive continuous functionε:M→(0,∞)and eachr>0, there exists aC1-smooth Lipschitz functiong:M→ℝsuch that|f(x)-g(x)|≤ε(x), for everyx∈M, andLip(g)≤Lip(f)+r. As a consequence, we derive a completeness criterium in the class of what we call quasi-reversible Finsler manifolds. Finally, considering the normed algebraCb1(M)of allC1functions with b

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38

Zeng, Fanqi, and Qun He. "Gradient estimates for a nonlinear heat equation under the Finsler-Ricci flow." Mathematica Slovaca 69, no. 2 (2019): 409–24. http://dx.doi.org/10.1515/ms-2017-0233.

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Abstract This paper considers a compact Finsler manifold (Mn, F(t), m) evolving under the Finsler-Ricci flow and establishes global gradient estimates for positive solutions of the following nonlinear heat equation: $$\begin{array}{} \partial_{t}u=\Delta_{m} u, \end{array} $$ where Δm is the Finsler-Laplacian. As applications, several Harnack inequalities are obtained.

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39

GUO, ENLI, HUAIFU LIU, and XIAOHUAN MO. "ON SPHERICALLY SYMMETRIC FINSLER METRICS WITH ISOTROPIC BERWALD CURVATURE." International Journal of Geometric Methods in Modern Physics 10, no. 10 (2013): 1350054. http://dx.doi.org/10.1142/s0219887813500540.

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A Finsler metric F is said to be spherically symmetric if the orthogonal group O(n) acts as isometries of F. In this paper, we show that every spherically symmetric Finsler metric of isotropic Berwald curvature is a Randers metric. We also construct explicitly a lot of new isotropic Berwald spherically symmetric Finsler metrics.

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40

Li, Benling, and Zhongmin Shen. "On a class of locally projectively flat Finsler metrics." International Journal of Mathematics 27, no. 06 (2016): 1650052. http://dx.doi.org/10.1142/s0129167x1650052x.

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Locally projectively flat Finsler metrics compose an important group of metrics in Finsler geometry. The characterization of these metrics is the regular case of the Hilbert’s Fourth Problem. In this paper, we study a class of Finsler metrics composed by a Riemann metric [Formula: see text] and a [Formula: see text]-form [Formula: see text] called general ([Formula: see text], [Formula: see text])-metrics. We classify those locally projectively flat when [Formula: see text] is projectively flat. By solving the corresponding nonlinear PDEs, the metrics in this class are totally determined. Then

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41

BUCATARU, IOAN, and ZOLTÁN MUZSNAY. "FINSLER METRIZABLE ISOTROPIC SPRAYS AND HILBERT’S FOURTH PROBLEM." Journal of the Australian Mathematical Society 97, no. 1 (2014): 27–47. http://dx.doi.org/10.1017/s1446788714000111.

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AbstractIt is well known that a system of homogeneous second-order ordinary differential equations (spray) is necessarily isotropic in order to be metrizable by a Finsler function of scalar flag curvature. In our main result we show that the isotropy condition, together with three other conditions on the Jacobi endomorphism, characterize sprays that are metrizable by Finsler functions of scalar flag curvature. We call these conditions the scalar flag curvature (SFC) test. The proof of the main result provides an algorithm to construct the Finsler function of scalar flag curvature, in the case

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Silva, J. E. G., R. V. Maluf, and C. A. S. Almeida. "Bipartite-Finsler symmetries." Physics Letters B 798 (November 2019): 135009. http://dx.doi.org/10.1016/j.physletb.2019.135009.

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Melonakos, J., E. Pichon, S. Angenent, and A. Tannenbaum. "Finsler Active Contours." IEEE Transactions on Pattern Analysis and Machine Intelligence 30, no. 3 (2008): 412–23. http://dx.doi.org/10.1109/tpami.2007.70713.

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Kouretsis, A. P., M. Stathakopoulos, and P. C. Stavrinos. "Relativistic Finsler geometry." Mathematical Methods in the Applied Sciences 37, no. 2 (2013): 223–29. http://dx.doi.org/10.1002/mma.2919.

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Mercaldo, Anna, Megumi Sano, and Futoshi Takahashi. "Finsler Hardy inequalities." Mathematische Nachrichten 293, no. 12 (2020): 2370–98. http://dx.doi.org/10.1002/mana.201900117.

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Fukui, Masaki. "Complex Finsler manifolds." Journal of Mathematics of Kyoto University 29, no. 4 (1989): 609–24. http://dx.doi.org/10.1215/kjm/1250520177.

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Ohta, Shin-ichi. "Finsler interpolation inequalities." Calculus of Variations and Partial Differential Equations 36, no. 2 (2009): 211–49. http://dx.doi.org/10.1007/s00526-009-0227-4.

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Guo, Enli, and Xiaohuan Mo. "Riemann-Finsler geometry." Frontiers of Mathematics in China 1, no. 4 (2006): 485–98. http://dx.doi.org/10.1007/s11464-006-0023-9.

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Youssef, Nabil L., and S. G. Elgendi. "New Finsler package." Computer Physics Communications 185, no. 3 (2014): 986–97. http://dx.doi.org/10.1016/j.cpc.2013.10.024.

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Caponio, Erasmo, and Antonio Masiello. "Harmonic Coordinates for the Nonlinear Finsler Laplacian and Some Regularity Results for Berwald Metrics." Axioms 8, no. 3 (2019): 83. http://dx.doi.org/10.3390/axioms8030083.

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We prove existence of harmonic coordinates for the nonlinear Laplacian of a Finsler manifold and apply them in a proof of the Myers–Steenrod theorem for Finsler manifolds. Different from the Riemannian case, these coordinates are not suitable for studying optimal regularity of the fundamental tensor, nevertheless, we obtain some partial results in this direction when the Finsler metric is Berwald.

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