On Geodesic Completeness of Nondegenerate Submanifolds in Semi-Euclidean Spaces

DOI

10.1142/S1402925109000200How to use a DOI?

Keywords

Nondegenerate submanifold; semi-Euclidean spaces; geodesic completeness; affine growth condition; second fundamental form tensor; nonacute geodesic; nonobtuse geodesic; totally umbilic

Abstract

In this paper, we study the geodesic completeness of nondegenerate submanifolds in semi-Euclidean spaces by extending the study of Beem and Ehrlich [1] to semi-Euclidean spaces. From the physical point of view, this extend may have a significance that a semi-Euclidean space contains more variety of Lorentzian submanifolds rather than those of Lorentzian hypersurfaces in a Minkowski space as in [1]. From mathematical point of view, since there is no distinction in the analysis of geodesic completeness of Lorentzian submanifolds and nondegenerate submanifolds in a semi-Euclidean space, we treat the mathematically more general case of nondegenerate submanifolds in a semi-Euclidean space. The new ideas leading to this generalization are the sufficient conditions for algorithms in the proofs of the results in [1]. Indeed these sufficient conditions for the algorithms also work well for the nondegenerate submanifolds in a semi-Euclidean space.

Copyright

© 2009 The Authors. Published by Atlantis Press and Taylor & Francis

Open Access

This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - JOUR
AU  - Fazilet Erkekog˜lu
PY  - 2021
DA  - 2021/01/07
TI  - On Geodesic Completeness of Nondegenerate Submanifolds in Semi-Euclidean Spaces
JO  - Journal of Nonlinear Mathematical Physics
SP  - 161
EP  - 168
VL  - 16
IS  - 2
SN  - 1776-0852
UR  - https://doi.org/10.1142/S1402925109000200
DO  - 10.1142/S1402925109000200
ID  - Erkekog˜lu2021
ER  -