The relations among two transversal submanifolds and global manifold

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dc.creatorYang, Guo-Hong
dc.creatorNi, Guang-Jiong
dc.creatorDuan, Yi-Shi
dc.date1999-01-27
dc.date.accessioned2026-07-07T03:32:56Z
dc.date.available2026-07-07T03:32:56Z
dc.descriptionIn Riemann geometry, the relations among two transversal submanifolds and global manifold are discussed. 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 linked together. When the inner product of the two tangent vectors 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 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. In general speaking, a submanifold is closely related to the matter fields of the other submanifold through the above inner product. This conclusion is in agreement with the Kaluza-Klein theory and it can be applied to generalize the models of direct product of manifolds in string and D-brane theories to the more general cases --- nondirect product manifolds.
dc.description18pages, LaTex, no figure
dc.identifierhttps://arxiv.org/abs/gr-qc/9901078
dc.identifierhttp://arxiv.org/abs/gr-qc/9901078
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/36422
dc.subjectGeneral Relativity and Quantum Cosmology
dc.subjectMathematical Physics
dc.subjectDifferential Geometry
dc.subjectGeometric Topology
dc.titleThe relations among two transversal submanifolds and global manifold
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