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Relevant bibliographies by topics / Submanifolds theory

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Academic literature on the topic 'Submanifolds theory'

Author: Grafiati

Published: 14 March 2023

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Journal articles on the topic "Submanifolds theory"

1

Jain, Varun, Amrinder Pal Singh, and Rakesh Kumar. "On the geometry of lightlike submanifolds of indefinite statistical manifolds." International Journal of Geometric Methods in Modern Physics 17, no. 07 (2020): 2050099. http://dx.doi.org/10.1142/s0219887820500991.

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We study lightlike submanifolds of indefinite statistical manifolds. Contrary to the classical theory of submanifolds of statistical manifolds, lightlike submanifolds of indefinite statistical manifolds need not to be statistical submanifold. Therefore, we obtain some conditions for a lightlike submanifold of indefinite statistical manifolds to be a lightlike statistical submanifold. We derive the expression of statistical sectional curvature and finally obtain some conditions for the induced statistical Ricci tensor on a lightlike submanifold of indefinite statistical manifolds to be symmetric.

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2

YANG, GUO-HONG, SHI-XIANG FENG, GUANG-JIONG NI, and YI-SHI DUAN. "RELATIONS OF TWO TRANSVERSAL SUBMANIFOLDS AND GLOBAL MANIFOLD." International Journal of Modern Physics A 16, no. 21 (2001): 3535–51. http://dx.doi.org/10.1142/s0217751x01005080.

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In Riemann geometry, the relations of two transversal submanifolds and global manifold are discussed without any concrete models. By replacing the normal vector of a submanifold with the tangent vector of another submanifold, the metric tensors, Christoffel symbols and curvature tensors of the three manifolds are connected at the intersection points of the two submanifolds. When the inner product of the two tangent vectors of submanifolds vanishes, some corollaries of these relations give the most important second fundamental form and Gauss–Codazzi equation in the conventional submanifold theory. As a special case, the global manifold which is Euclidean is considered. It is pointed out that, in order to obtain the nonzero energy–momentum tensor of matter field in a submanifold, there must be the contributions of the above inner product and the other submanifold. Generally speaking, a submanifold is closely related to the matter fields of the other submanifold and the two submanifolds affect each other through the above inner product.

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3

MONTE, EDMUNDO M. "MATHEMATICAL SUPPORT TO BRANEWORLD THEORY." International Journal of Geometric Methods in Modern Physics 04, no. 08 (2007): 1259–67. http://dx.doi.org/10.1142/s0219887807002557.

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The braneworld theory appear with the purpose of solving the problem of the hierarchy of the fundamental interactions. The perspectives of the theory emerge as a new physics, for example, deviation of the law of Newton's gravity. One of the principles of the theory is to suppose that the braneworld is local submanifold in a space of high dimension, the bulk, solution of Einstein's equations in high dimension. In this paper we approach the mathematical consistency of this theory with a new proof of the fundamental theorem of submanifolds for the case of semi-Riemannian manifolds. This theorem consists of an essential mathematical support for this new theory. We find the integrability conditions for the existence of space–time submanifolds in a pseudo-Euclidean space.

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4

Wu, B. Y. "Some results on Finsler submanifolds." International Journal of Mathematics 27, no. 03 (2016): 1650021. http://dx.doi.org/10.1142/s0129167x1650021x.

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In this paper we study the submanifold theory in terms of Chern connection. We introduce the notions of the second fundamental form and mean curvature for Finsler submanifolds, and establish the fundamental equations by means of moving frame for the hypersurface case. We provide the estimation of image radius for compact submanifold, and prove that there exists no compact minimal submanifold in any complete noncompact and simply connected Finsler manifold with nonpositive flag curvature. We also characterize the Minkowski hyperplanes, Minkowski hyperspheres and Minkowski cylinders as the only hypersurfaces in Minkowski space with parallel second fundamental form.

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5

Varolin, Dror. "A Takayama-type extension theorem." Compositio Mathematica 144, no. 2 (2008): 522–40. http://dx.doi.org/10.1112/s0010437x07002989.

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AbstractWe prove a theorem on the extension of holomorphic sections of powers of adjoint bundles from submanifolds of complex codimension 1 having non-trivial normal bundle. The first such result, due to Takayama, considers the case where the canonical bundle is twisted by a line bundle that is a sum of a big and nef line bundle and a $\mathbb {Q}$-divisor that has Kawamata log terminal singularities on the submanifold from which extension occurs. In this paper we weaken the positivity assumptions on the twisting line bundle to what we believe to be the minimal positivity hypotheses. The main new idea is an L2 extension theorem of Ohsawa–Takegoshi type, in which twisted canonical sections are extended from submanifolds with non-trivial normal bundle.

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6

Ali, Akram, Wan Othman, and Sayyadah Qasem. "Geometric inequalities for CR-warped product submanifolds of locally conformal almost cosymplectic manifolds." Filomat 33, no. 3 (2019): 741–48. http://dx.doi.org/10.2298/fil1903741a.

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In this paper, we establish some inequalities for the squared norm of the second fundamental form and the warping function of warped product submanifolds in locally conformal almost cosymplectic manifolds with pointwise ?-sectional curvature. The equality cases are also considered. Moreover, we prove a triviality result for CR-warped product submanifold by using the integration theory on a compact orientate manifold without boundary.

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7

Biard, Séverine, and Emil J. Straube. "L2-Sobolev theory for the complex Green operator." International Journal of Mathematics 28, no. 09 (2017): 1740006. http://dx.doi.org/10.1142/s0129167x17400067.

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These notes are concerned with the [Formula: see text]-Sobolev theory of the complex Green operator on pseudoconvex, oriented, bounded and closed Cauchy–Riemann (CR)-submanifolds of [Formula: see text] of hypersurface type. This class of submanifolds generalizes that of boundaries of pseudoconvex domains. We first discuss briefly the CR-geometry of general CR-submanifolds and then specialize to this class. Next, we review the basic [Formula: see text]-theory of the tangential CR operator and the associated complex Green operator(s) on these submanifolds. After these preparations, we discuss recent results on compactness and regularity in Sobolev spaces of the complex Green operator(s).

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8

Urban, Zbyněk, and Ján Brajerčík. "The fundamental Lepage form in variational theory for submanifolds." International Journal of Geometric Methods in Modern Physics 15, no. 06 (2018): 1850103. http://dx.doi.org/10.1142/s0219887818501037.

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The multiple-integral variational functionals for finite-dimensional immersed submanifolds are studied by means of the fundamental Lepage equivalent of a homogeneous Lagrangian, which can be regarded as a generalization of the well-known Hilbert form in the classical mechanics. The notion of a Lepage form is extended to manifolds of regular velocities and plays a basic role in formulation of the variational theory for submanifolds. The theory is illustrated on the minimal submanifolds problem, including analysis of conservation law equations.

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9

Mihai, Ion, and Radu-Ioan Mihai. "A New Algebraic Inequality and Some Applications in Submanifold Theory." Mathematics 9, no. 11 (2021): 1175. http://dx.doi.org/10.3390/math9111175.

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We give a simple proof of the Chen inequality involving the Chen invariant δ(k) of submanifolds in Riemannian space forms. We derive Chen’s first inequality and the Chen–Ricci inequality. Additionally, we establish a corresponding inequality for statistical submanifolds.

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10

Urban, Zbyněk, and Demeter Krupka. "Foundations of higher-order variational theory on Grassmann fibrations." International Journal of Geometric Methods in Modern Physics 11, no. 07 (2014): 1460023. http://dx.doi.org/10.1142/s0219887814600238.

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A setting for higher-order global variational analysis on Grassmann fibrations is presented. The integral variational principles for one-dimensional immersed submanifolds are introduced by means of differential 1-forms with specific properties, similar to the Lepage forms from the variational calculus on fibred manifolds. Prolongations of immersions and vector fields to the Grassmann fibrations are defined as a geometric tool for the variations of immersions, and the first variation formula in the infinitesimal form is derived. Its consequences, the Euler–Lagrange equations for submanifolds and the Noether theorem on invariant variational functionals are proved. Examples clarifying the meaning of the Noether theorem in the context of variational principles for submanifolds are given.

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