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Journal articles on the topic 'Codazzi'

Author: Grafiati

Published: 4 June 2021

Last updated: 16 February 2022

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1

Peyghan, E., and C. Arcuş. "Codazzi and statistical connections on almost product manifolds." Filomat 34, no. 13 (2020): 4343–58. http://dx.doi.org/10.2298/fil2013343p.

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Considering an almost product manifold, we get the necessary and sufficient conditions for Codazzi connections on it. Also, we show that a Codazzi adapted connection on an almost product manifold, gives two type of Codazzi connections on it?s distributions, and moreover we study the conditions of holding the converse of this. Finally, we study the Codazzi (and statistical) structures for Schouten-Van Kampen and Vr?nceanu connections as two important special cases of adapted connections, and then we present some important examples of them.

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2

Etayo, Fernando, Araceli deFrancisco, and Rafael Santamaría. "There are no genuine Kähler–Codazzi manifolds." International Journal of Geometric Methods in Modern Physics 17, no. 03 (February 14, 2020): 2050044. http://dx.doi.org/10.1142/s0219887820500449.

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Nearly Kähler- and Kähler–Codazzi-type manifolds are defined in a very similar way. We prove that nearly Kähler-type manifolds make sense only in Hermitian and para-Hermitian contexts, and that Kähler–Codazzi-type manifolds reduce to Kähler-type manifolds in all the four Hermitian, para-Hermitian, Norden and product Riemannian geometries. Kähler–Codazzi condition is also studied on almost complex golden manifolds.

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3

Schwenk-Schellschmidt, Angela, Udo Simon, and Luc Vrancken. "Codazzi-equivalent Riemannian Metrics." Asian Journal of Mathematics 14, no. 3 (2010): 291–302. http://dx.doi.org/10.4310/ajm.2010.v14.n3.a1.

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4

Hasanis, Thomas, and Theodoros Vlachos. "Hypersurfaces and Codazzi tensors." Monatshefte für Mathematik 154, no. 1 (March 3, 2008): 51–58. http://dx.doi.org/10.1007/s00605-008-0528-2.

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5

Schwenk-Schellschmidt, Angela, and Udo Simon. "Codazzi-Equivalent Affine Connections." Results in Mathematics 56, no. 1-4 (September 11, 2009): 211–29. http://dx.doi.org/10.1007/s00025-009-0420-y.

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6

Conte, Robert, and A. Michel Grundland. "Reductions of Gauss-Codazzi Equations." Studies in Applied Mathematics 137, no. 3 (March 8, 2016): 306–27. http://dx.doi.org/10.1111/sapm.12121.

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7

KANEDA, Eiji. "On the Gauss-Codazzi equations." Hokkaido Mathematical Journal 19, no. 2 (June 1990): 189–213. http://dx.doi.org/10.14492/hokmj/1381517355.

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8

An-Min, Li. "Some theorems on Codazzi tensors." Mathematische Zeitschrift 191, no. 4 (December 1986): 575–84. http://dx.doi.org/10.1007/bf01162347.

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9

Aledo, Juan A., José M. Espinar, and José A. Gálvez. "The Codazzi equation for surfaces." Advances in Mathematics 224, no. 6 (August 2010): 2511–30. http://dx.doi.org/10.1016/j.aim.2010.02.007.

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10

Catino, Giovanni, Carlo Mantegazza, and Lorenzo Mazzieri. "A note on Codazzi tensors." Mathematische Annalen 362, no. 1-2 (November 22, 2014): 629–38. http://dx.doi.org/10.1007/s00208-014-1135-2.

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11

Ariwahjoedi, Seramika, Jusak Sali Kosasih, Carlo Rovelli, and Freddy P. Zen. "Curvatures and discrete Gauss–Codazzi equation in (2 + 1)-dimensional loop quantum gravity." International Journal of Geometric Methods in Modern Physics 12, no. 10 (October 25, 2015): 1550112. http://dx.doi.org/10.1142/s0219887815501121.

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We derive the Gauss–Codazzi equation in the holonomy and plane-angle representations and we use the result to write a Gauss–Codazzi equation for a discrete (2 + 1)-dimensional manifold, triangulated by isosceles tetrahedra. This allows us to write operators acting on spin network states in (2 + 1)-dimensional loop quantum gravity, representing the 3-dimensional intrinsic, 2-dimensional intrinsic, and 2-dimensional extrinsic curvatures.

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12

Suh, Young Jin. "Real hypersurfaces in the complex quadric with Reeb parallel shape operator." International Journal of Mathematics 25, no. 06 (June 2014): 1450059. http://dx.doi.org/10.1142/s0129167x14500591.

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First, we introduce the notion of shape operator of Codazzi type for real hypersurfaces in the complex quadric Qm = SOm+2/SOmSO2. Next, we give a complete proof of non-existence of real hypersurfaces in Qm = SOm+2/SOmSO2 with shape operator of Codazzi type. Motivated by this result we have given a complete classification of real hypersurfaces in Qm = SOm+2/SOmSO2 with Reeb parallel shape operator.

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13

Merton, Gabe. "Codazzi tensors with two eigenvalue functions." Proceedings of the American Mathematical Society 141, no. 9 (May 16, 2013): 3265–73. http://dx.doi.org/10.1090/s0002-9939-2013-11616-3.

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14

Sánchez, Efraín. "Nancy Appelbaum. Dibujar la nación. La Comisión Corográfica en la Colombia del siglo XIX." Anuario Colombiano de Historia Social y de la Cultura 47, no. 1 (January 1, 2020): 404–7. http://dx.doi.org/10.15446/achsc.v47n1.83213.

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La Comisión Corográfica, dirigida por el geógrafo militar italiano Agustín Codazzi, fue una empresa patrocinada por el gobierno a mediados del siglo XIX para hacer, por primera vez, el levantamiento sistemático y oficial de los mapas de Colombia y sus provincias, así como sus correspondientes descripciones geográficas. Láminas de vistas, paisajes y costumbres, una extensa producción botánica, informes especiales sobre mejoras materiales y relatos de las expediciones, complementan el vasto legado cartográfico y geográfico de aquella empresa. Valga agregar que quien escribe estas líneas llevó a cabo el primer estudio pormenorizado de los antecedentes, los fundamentos y motivos, los trabajos de campo y el conjunto de la obra de la Comisión Corográfica (Efraín Sánchez, Gobierno y geografía: Agustín Codazzi y la Comisión Corográfica de la Nueva Granada. Bogotá: Banco de la República / El Áncora Editores, 1999). Desde entonces se han realizado otros esfuerzos, sin duda importantes, pero el libro de Nancy Appelbaum es el primer intento sistemático por profundizar en aspectos significativos de la obra de Codazzi, sus colaboradores y seguidores.

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15

Ando, Naoya. "Semisurfaces and the equations of Codazzi-Mainardi." Tsukuba Journal of Mathematics 30, no. 1 (June 2006): 1–30. http://dx.doi.org/10.21099/tkbjm/1496165026.

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16

Salimov, Arif, and Sibel Turanli. "Curvature properties of anti-Kähler–Codazzi manifolds." Comptes Rendus Mathematique 351, no. 5-6 (March 2013): 225–27. http://dx.doi.org/10.1016/j.crma.2013.03.008.

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17

Saban, Giacomo. "Alcune considerazioni elementari sulle coppie di Codazzi." Rendiconti del Seminario Matematico e Fisico di Milano 54, no. 1 (December 1985): 225–37. http://dx.doi.org/10.1007/bf02924859.

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18

Pérez, Juan de Dios, Florentino G. Santos, and Young Jin Suh. "Real Hypersurfaces in Complex Projective Space Whose Structure Jacobi Operator Is of Codazzi Type." Canadian Mathematical Bulletin 50, no. 3 (September 1, 2007): 347–55. http://dx.doi.org/10.4153/cmb-2007-033-9.

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19

Stepanov, S., and I. Tsyganok. "Vanishing theorems for higher-order Killing and Codazzi." Differential Geometry of Manifolds of Figures, no. 50 (2019): 141–47. http://dx.doi.org/10.5922/0321-4796-2019-50-16.

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A Killing p-tensor (for an arbitrary natural number p ≥ 2) is a symmetric p-tensor with vanishing symmetrized covariant derivative. On the other hand, Codazzi p-tensor is a symmetric p-tensor with symmetric covariant derivative. Let M be a complete and simply connected Riemannian manifold of nonpositive (resp. non-negative) sectional curvature. In the first case we prove that an arbitrary symmetric traceless Killing p-tensor is parallel on M if its norm is a Lq -function for some q > 0. If in addition the volume of this manifold is infinite, then this tensor is equal to zero. In the second case we prove that an arbitrary traceless Codazzi p-tensor is equal to zero on a noncompact manifold M if its norm is a Lq -function for some q  1 .

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20

Cheshkova, M. A. "The deformation algebra associated with a Codazzi field." Siberian Mathematical Journal 31, no. 5 (1991): 859–62. http://dx.doi.org/10.1007/bf00974505.

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21

Fei, Teng, and Jun Zhang. "Interaction of Codazzi Couplings with (Para-)Kähler Geometry." Results in Mathematics 72, no. 4 (July 5, 2017): 2037–56. http://dx.doi.org/10.1007/s00025-017-0711-7.

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22

Mincic, Svetislav, Ljubica Velimirovic, and Mica Stankovic. "New integrability conditions of derivational equations of a submanifold in a generalized Riemannian space." Filomat 24, no. 4 (2010): 137–46. http://dx.doi.org/10.2298/fil1004137m.

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The present work is a continuation of [5] and [6]. In [5] we have obtained derivational equations of a submanifold XM of a generalized Riemannian space GRN. Since the basic tensor in GRN is asymmetric and in this way the connection is also asymmetric, in a submanifold the connection is generally asymmetric too. By reason of this, we define 4 kinds of covariant derivative and obtain 4 kinds of derivational equations. In [6] we have obtained integrability conditions and Gauss-Codazzi equations using the 1st and the 2st kind of covariant derivative. The present work deals in the cited matter, using the 3rd and the 4th kind of covariant derivative. One obtains three new integrability conditions for derivational equations of tangents and three such conditions for normals of the submanifold, as the corresponding Gauss-Codazzi equations too.

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23

Calviño-Louzao, E., E. García-Río, J. Seoane-Bascoy, and R. Vázquez-Lorenzo. "Three-dimensional manifolds with special Cotton tensor." International Journal of Geometric Methods in Modern Physics 12, no. 01 (December 28, 2014): 1550005. http://dx.doi.org/10.1142/s021988781550005x.

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The Cotton tensor of three-dimensional Walker manifolds is investigated. A complete description of all locally conformally flat Walker three-manifolds is given, as well as that of Walker manifolds whose Cotton tensor is either a Codazzi or a Killing tensor.

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24

WANG, PEI. "KALUZA–KLEIN DIMENSIONAL REDUCTION AND GAUSS–CODAZZI–RICCI EQUATIONS." International Journal of Modern Physics A 24, no. 06 (March 10, 2009): 1207–20. http://dx.doi.org/10.1142/s0217751x09042967.

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In this paper we imitate the traditional method which is used customarily in the general relativity and some mathematical literatures to derive the Gauss–Codazzi–Ricci equations for dimensional reduction. It would be more distinct concerning geometric meaning than the vielbein method. Especially, if the lower-dimensional metric is independent of reduced dimensions the counterpart of the symmetric extrinsic curvature is proportional to the antisymmetric Kaluza–Klein gauge field strength. For isometry group of internal space, the SO (n) symmetry and SU (n) symmetry are discussed. And the Kaluza–Klein instanton is also enquired.

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25

沈, 一兵. "二维球面上的Codazzi张量." Chinese Science Bulletin 37, no. 6 (March 1, 1992): 481–84. http://dx.doi.org/10.1360/csb1992-37-6-481.

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26

Salimov, Arif, Kursat Akbulut, and Sibel Turanli. "On an isotropic property of anti-Kähler–Codazzi manifolds." Comptes Rendus Mathematique 351, no. 21-22 (November 2013): 837–39. http://dx.doi.org/10.1016/j.crma.2013.09.020.

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27

Shen, Yi Bing. "Harmonic Gauss maps and Codazzi tensors for affine hypersurfaces." Archiv der Mathematik 55, no. 3 (September 1990): 298–305. http://dx.doi.org/10.1007/bf01191173.

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28

Marugame, Taiji. "GJMS operators and Q-curvature for conformal Codazzi structures." Differential Geometry and its Applications 49 (December 2016): 176–96. http://dx.doi.org/10.1016/j.difgeo.2016.08.001.

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29

Calvaruso, Giovanni. "Riemannian 3-metrics with a generic Codazzi Ricci tensor." Geometriae Dedicata 151, no. 1 (September 5, 2010): 259–67. http://dx.doi.org/10.1007/s10711-010-9532-5.

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30

Dajczer, Marcos, and Ruy Tojeiro. "Commuting Codazzi tensors and the Ribaucour transformation for submanifolds." Results in Mathematics 44, no. 3-4 (November 2003): 258–78. http://dx.doi.org/10.1007/bf03322986.

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31

Cao, Wentao. "Global BV entropy solutions to the Gauss–Codazzi system." Journal of Mathematical Analysis and Applications 444, no. 2 (December 2016): 1015–26. http://dx.doi.org/10.1016/j.jmaa.2016.07.006.

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32

Shandra, Igor G., Sergey E. Stepanov, and Josef Mikeš. "On higher-order Codazzi tensors on complete Riemannian manifolds." Annals of Global Analysis and Geometry 56, no. 3 (July 6, 2019): 429–42. http://dx.doi.org/10.1007/s10455-019-09673-w.

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33

Baum, Helga, and Olaf Müller. "Codazzi spinors and globally hyperbolic manifolds with special holonomy." Mathematische Zeitschrift 258, no. 1 (May 12, 2007): 185–211. http://dx.doi.org/10.1007/s00209-007-0169-5.

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34

Stepanov, S. E., and I. I. Tsyganok. "Codazzi and Killing Tensors on a Complete Riemannian Manifold." Mathematical Notes 109, no. 5-6 (May 2021): 932–39. http://dx.doi.org/10.1134/s0001434621050266.

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35

Bracken, Paul. "Quaternionic representation of the moving frame for surfaces in Euclidean three-space and Lax pair." International Journal of Mathematics and Mathematical Sciences 2004, no. 15 (2004): 755–62. http://dx.doi.org/10.1155/s0161171204310392.

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The moving frame and associated Gauss-Codazzi equations for surfaces in three-space are introduced. A quaternionic representation is used to identify the Gauss-Weingarten equation with a particular Lax representation. Several examples are given, such as the case of constant mean curvature.

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36

ROTH, JULIEN. "A NEW RESULT ABOUT ALMOST UMBILICAL HYPERSURFACES OF REAL SPACE FORMS." Bulletin of the Australian Mathematical Society 91, no. 1 (October 14, 2014): 145–54. http://dx.doi.org/10.1017/s0004972714000732.

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AbstractIn this short note, we prove that an almost umbilical compact hypersurface of a real space form with almost Codazzi umbilicity tensor is embedded, diffeomorphic and quasi-isometric to a round sphere. Then, we derive a new characterisation of geodesic spheres in space forms.

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37

Ünal, İnan. "Generalized Quasi-Einstein Manifolds in Contact Geometry." Mathematics 8, no. 9 (September 16, 2020): 1592. http://dx.doi.org/10.3390/math8091592.

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In this study, we investigate generalized quasi-Einstein normal metric contact pair manifolds. Initially, we deal with the elementary properties and existence of generalized quasi-Einstein normal metric contact pair manifolds. Later, we explore the generalized quasi-constant curvature of normal metric contact pair manifolds. It is proved that a normal metric contact pair manifold with generalized quasi-constant curvature is a generalized quasi-Einstein manifold. Normal metric contact pair manifolds satisfying cyclic parallel Ricci tensor and the Codazzi type of Ricci tensor are considered, and further prove that a generalized quasi-Einstein normal metric contact pair manifold does not satisfy Codazzi type of Ricci tensor. Finally, we characterize normal metric contact pair manifolds satisfying certain curvature conditions related to M-projective, conformal, and concircular curvature tensors. We show that a normal metric contact pair manifold with generalized quasi-constant curvature is locally isometric to the Hopf manifold S2n+1(1)×S1.

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38

Li, Yanlin, Akram Ali, and Rifaqat Ali. "A General Inequality for CR-Warped Products in Generalized Sasakian Space Form and Its Applications." Advances in Mathematical Physics 2021 (August 9, 2021): 1–6. http://dx.doi.org/10.1155/2021/5777554.

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In the present paper, by considering the Gauss equation in place of the Codazzi equation, we derive new optimal inequality for the second fundamental form of CR-warped product submanifolds into a generalized Sasakian space form. Moreover, the inequality generalizes some inequalities for various ambient space forms.

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39

Mussel, Matan, and Marshall Slemrod. "Conservation laws in biology: Two new applications." Quarterly of Applied Mathematics 79, no. 3 (March 25, 2021): 479–92. http://dx.doi.org/10.1090/qam/1590.

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This paper provides two new applications of conservation laws in biology. The first is the application of the van der Waals fluid formalism for action potentials. The second is the application of the conservation laws of differential geometry (Gauss–Codazzi equations) to produce non-smooth surfaces representing Endoplasmic Reticulum sheets.

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40

Arroyo, Josu, Óscar J. Garay, and Álvaro Pámpano. "Binormal Motion of Curves with Constant Torsion in 3-Spaces." Advances in Mathematical Physics 2017 (2017): 1–8. http://dx.doi.org/10.1155/2017/7075831.

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We study curve motion by the binormal flow with curvature and torsion depending velocity and sweeping out immersed surfaces. Using the Gauss-Codazzi equations, we obtain filaments evolving with constant torsion which arise from extremal curves of curvature energy functionals. They are “soliton” solutions in the sense that they evolve without changing shape.

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41

Blažić, Novica, Neda Bokan, and Peter B. Gilkey. "Pontrjagin forms, Chern Simons classes, Codazzi transformations, and affine hypersurfaces." Journal of Geometry and Physics 27, no. 3-4 (September 1998): 333–49. http://dx.doi.org/10.1016/s0393-0440(98)00005-9.

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42

Marshall, David. "A View of Poggioreale by Viviano Codazzi and Domenico Gargiulo." Journal of the Society of Architectural Historians 45, no. 1 (March 1, 1986): 32–46. http://dx.doi.org/10.2307/990127.

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This study attempts to establish the extent to which a painting by Viviano Codazzi and Domenico Gargiulo of the villa Poggioreale as an architectural capriccio can be used as a record of the appearance of the villa in the mid-17th century. By correlating the painting with the plan of the villa in the Carafa map and the Baratta view, a new reconstruction of the layout of the villa garden is proposed.

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43

Abdalla, M. C. B., M. E. X. Guimarães, and J. M. Hoff da Silva. "Gauss–Codazzi formalism to brane-world within Brans–Dicke theory." European Physical Journal C 55, no. 2 (April 15, 2008): 337–42. http://dx.doi.org/10.1140/epjc/s10052-008-0577-7.

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44

Ceyhan, Ö., A. S. Fokas, and M. Gürses. "Deformations of surfaces associated with integrable Gauss–Mainardi–Codazzi equations." Journal of Mathematical Physics 41, no. 4 (April 2000): 2251–70. http://dx.doi.org/10.1063/1.533237.

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45

Bilen, Lokman, Sibel Turanli, and Aydin Gezer. "On Kähler–Norden–Codazzi golden structures on pseudo-Riemannian manifolds." International Journal of Geometric Methods in Modern Physics 15, no. 05 (April 2, 2018): 1850080. http://dx.doi.org/10.1142/s0219887818500809.

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In this paper, we consider a pseudo-Riemannian manifold equipped with a Kähler–Norden–Codazzi golden structure. For such a manifold, we study curvature properties. Also, we define special connections of the first type and of the second type on the manifold, which preserve the associated twin Norden golden metric and satisfy some special conditions and present some results concerning them.

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46

Pinkall, U., A. Schwenk-Schellschmidt, and U. Simon. "Geometric methods for solving Codazzi and Monge-Amp�re equations." Mathematische Annalen 298, no. 1 (January 1994): 89–100. http://dx.doi.org/10.1007/bf01459727.

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47

Christoforou, Cleopatra. "BV weak solutions to Gauss–Codazzi system for isometric immersions." Journal of Differential Equations 252, no. 3 (February 2012): 2845–63. http://dx.doi.org/10.1016/j.jde.2011.08.046.

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48

Jelonek, Włodzimierz. "Characterization of affine ruled surfaces." Glasgow Mathematical Journal 39, no. 1 (January 1997): 17–20. http://dx.doi.org/10.1017/s0017089500031852.

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The aim of this paper is to give certain conditions characterizing ruled affine surfaces in terms of the Blaschke structure (∇, h, S) induced on a surface (M, f) in ℝ3. The investigation of affine ruled surfaces was started by W. Blaschke in the beginning of our century (see [1]). The description of affine ruled surfaces can be also found in the book [11], [3] and [7]. Ruled extremal surfaces are described in [9]. We show in the present paper that a shape operator S is a Codazzi tensor with respect to the Levi-Civita connection ∇ of affine metric h if and only if (M, f) is an affine sphere or a ruled surface. Affine surfaces with ∇S = 0 are described in [2] (see also [4]). We also show that a surface which is not an affine sphere is ruled iff im(S - HI) =ker(S - HI) and ket(S - HI) ⊂ ker dH. Finally we prove that an affine surface with indefinite affine metric is a ruled affine sphere if and only if the difference tensor K is a Codazzi tensor with respect to ∇.

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49

Wu, Tong, and Yong Wang. "Codazzi Tensors and the Quasi-Statistical Structure Associated with Affine Connections on Three-Dimensional Lorentzian Lie Groups." Symmetry 13, no. 8 (August 9, 2021): 1459. http://dx.doi.org/10.3390/sym13081459.

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In this paper, we classify three-dimensional Lorentzian Lie groups on which Ricci tensors associated with Bott connections, canonical connections and Kobayashi–Nomizu connections are Codazzi tensors associated with these connections. We also classify three-dimensional Lorentzian Lie groups with the quasi-statistical structure associated with Bott connections, canonical connections and Kobayashi–Nomizu connections.

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50

Yasar, Erol, A. Ceylan Cöken, and Ahmet Yücesan. "Lightlike hypersurfaces in semi-Riemannian manifold with semi-symmetric non-metric connection." MATHEMATICA SCANDINAVICA 102, no. 2 (June 1, 2008): 253. http://dx.doi.org/10.7146/math.scand.a-15061.

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In this paper, we study lightlike hypersurfaces of a semi-Riemannian manifold admitting a semi-symmetric non-metric connection. We give the equations of Gauss and Codazzi. Then, we obtain conditions under which the Ricci tensor of a lightlike hypersurface is symmetric given that the ambient space is equipped with a semi-symmetric non-metric connection.

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