Journal of Nonlinear Mathematical Physics

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Volume 17, Issue Supplement 1, December 2010, Pages 49 - 70

On Invariants of Immersions of an n-Dimensional Manifold in an n-Dimensional Pseudo-Euclidean Space*

Authors
Djavvat Khadjiev
Department of Mathematics, Karadeniz Technical University, 61080, Trabzon, Turkey,khdjavvat@gmail.com
*

This work was supported by the Research Fund of TUBITAK. Project number:107T049.

Received 30 June 2008, Accepted 30 June 2009, Available Online 7 January 2021.
DOI
10.1142/S1402925110000799How to use a DOI?
Keywords
Immersion; invariant; pseudo-Riemannian metric; Riemannian curvature tensor
Abstract

Let Epn be the n-dimensional pseudo-Euclidean space of index p and M(n, p) the group of all transformations of Epn generated by pseudo-orthogonal transformations and parallel translations. We describe the system of generators of the differential field of all M(n, p)-invariant differential rational functions of a map x:J→Epn of an open subset J⊆Epn . Using this result, we prove analogues of the Bonnet theorem for immersions of an n-dimensional C∞-manifold J in Epn . These analogues are given in terms of the pseudo-Riemannian metric, the volume form, and the connection on J induced by the immersion of J in Epn .

Copyright
© 2010 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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Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
17 - Supplement 1
Pages
49 - 70
Publication Date
2021/01/07
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
10.1142/S1402925110000799How to use a DOI?
Copyright
© 2010 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/).

Cite this article

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TY  - JOUR
AU  - Djavvat Khadjiev
PY  - 2021
DA  - 2021/01/07
TI  - On Invariants of Immersions of an n-Dimensional Manifold in an n-Dimensional Pseudo-Euclidean Space*
JO  - Journal of Nonlinear Mathematical Physics
SP  - 49
EP  - 70
VL  - 17
IS  - Supplement 1
SN  - 1776-0852
UR  - https://doi.org/10.1142/S1402925110000799
DO  - 10.1142/S1402925110000799
ID  - Khadjiev2021
ER  -