The submanifolds
of the manifold
. II. Fundamental equations on
of ![<sup>*</sup>g-MEX<sub>n</sub>](http://siba-ese.unile.it/plugins/generic/latexRender/cache/6a7c8c7448e8301eb10d30e3900d2e08.png)
Abstract
In our previous paper [4], we studied the induced connection of the
-connection on a submanifold
embedded in a manifold
together with the generalized coefficients
of the second fundamental form of
, with emphasis on the proof of a necessary and sufficient condition for the induced connection of
in
to be a
-connection. This paper is a direct continuation of [4]. In this paper, we derive the generalized fundamental equations on
of
, such as the generalized Gauss formulae, the generalized Weingarten equations, and the Gauss-Codazzi equations. Furthermore, we also present surveyable tensorial representations of curvature tensors
of
and
of
.
![<sup>*</sup>g-Me](http://siba-ese.unile.it/plugins/generic/latexRender/cache/9a6ca8cc89769c6df8a3db681ccd84a7.png)
![X<sub>m</sub>](http://siba-ese.unile.it/plugins/generic/latexRender/cache/5eb59d2473eb56d7a56fb97c205e0ecc.png)
![<sup>*</sup>g-Mex<sub>n</sub>](http://siba-ese.unile.it/plugins/generic/latexRender/cache/87bf899c6442b0fa7092c3bbeaef8a58.png)
![ω_{ij}](http://siba-ese.unile.it/plugins/generic/latexRender/cache/3a2077ed62b85c674cb81cb7b00a163e.png)
![X<sub>m</sub>](http://siba-ese.unile.it/plugins/generic/latexRender/cache/5eb59d2473eb56d7a56fb97c205e0ecc.png)
![X<sub>m</sub>](http://siba-ese.unile.it/plugins/generic/latexRender/cache/5eb59d2473eb56d7a56fb97c205e0ecc.png)
![<sup>*</sup>g-MEX<sub>n</sub>](http://siba-ese.unile.it/plugins/generic/latexRender/cache/6a7c8c7448e8301eb10d30e3900d2e08.png)
![<sup>*</sup>g-ME](http://siba-ese.unile.it/plugins/generic/latexRender/cache/8fdd14fe53bf3f5b97a931a545e359e5.png)
![X<sub>m</sub>](http://siba-ese.unile.it/plugins/generic/latexRender/cache/5eb59d2473eb56d7a56fb97c205e0ecc.png)
![<sup>*</sup>g-MEX<sub>n</sub>](http://siba-ese.unile.it/plugins/generic/latexRender/cache/6a7c8c7448e8301eb10d30e3900d2e08.png)
![R<sup>\mu</sup>_{ω\muλ}](http://siba-ese.unile.it/plugins/generic/latexRender/cache/d6d082a2fc6823ebc4aad6ec60f1e5bd.png)
![<sup>*</sup>g-MEX<sub>n</sub>](http://siba-ese.unile.it/plugins/generic/latexRender/cache/6a7c8c7448e8301eb10d30e3900d2e08.png)
![R<sup>h</sup>_{ijk}](http://siba-ese.unile.it/plugins/generic/latexRender/cache/fcc8db3479bfec09e6307380e0c9cbfe.png)
![X<sub>m</sub>](http://siba-ese.unile.it/plugins/generic/latexRender/cache/5eb59d2473eb56d7a56fb97c205e0ecc.png)
DOI Code:
10.1285/i15900932v18n2p227
Full Text: PDF