The submanifolds
of the manifold
. I. The induced connection on
of ![*g-MEX<sub>n</sub>](http://siba-ese.unile.it/plugins/generic/latexRender/cache/43929ceed413ab1dd09f04bf87495f1e.png)
Abstract
An Einstein's connection which takes the form (2.33) is called an
-connection. Recently, Chung and et al ([15], 1993)introduced a new manifolds, called an n-dimensional
-manifold (debnoted by
).The manifold
is a generalized n-dimensional Riemannian manifold
on which the differential geometric structure is imposed by the unified field tensor
satisfying certain conditions through the
-connection. In the following series of two papers, we investigate the submanifolds
of
: I. The induced connection on
of
II. The generalized fundamental equations on
of
In this paper, Part I of the series, we present a brief introduction of n-dimensional
-unified field theory, the C-nonholonomic frame of reference in
at points of
, and the manifold
. and then, we introduce the generalized coefficients of the second fundamental form of
and prove a necessary and sufficient condition for the induced connection on
of
to be a
-connection. Our subsequent paper, Part II of the series, deals with the generalized fundamental equations on
of
, such as the generalized Gauss formulae, the generalized Weingarten equations, and the Gauss-Codazzi equations.
![<sup>*</sup>g-ME](http://siba-ese.unile.it/plugins/generic/latexRender/cache/8fdd14fe53bf3f5b97a931a545e359e5.png)
![<sup>*</sup>g-ME](http://siba-ese.unile.it/plugins/generic/latexRender/cache/8fdd14fe53bf3f5b97a931a545e359e5.png)
![<sup>*</sup>g-MEX<sub>n</sub>](http://siba-ese.unile.it/plugins/generic/latexRender/cache/6a7c8c7448e8301eb10d30e3900d2e08.png)
![<sup>*</sup>g-MEX<sub>n</sub>](http://siba-ese.unile.it/plugins/generic/latexRender/cache/6a7c8c7448e8301eb10d30e3900d2e08.png)
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![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)
![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)
![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](http://siba-ese.unile.it/plugins/generic/latexRender/cache/3d391296986db470256f9434ac0f8814.png)
![X<sub>n</sub>](http://siba-ese.unile.it/plugins/generic/latexRender/cache/71a21c55bdfd934b5e8942cfac4bbd88.png)
![X-m](http://siba-ese.unile.it/plugins/generic/latexRender/cache/7f644a08499a32bb3b1ee48bdfebe298.png)
![<sup>*</sup>g-MEX<sub>n</sub>](http://siba-ese.unile.it/plugins/generic/latexRender/cache/6a7c8c7448e8301eb10d30e3900d2e08.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>-MEX<sub>n</sub>](http://siba-ese.unile.it/plugins/generic/latexRender/cache/a539491ce8350aea0372ad655718116a.png)
![<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>-MEX<sub>n</sub>](http://siba-ese.unile.it/plugins/generic/latexRender/cache/a539491ce8350aea0372ad655718116a.png)
DOI Code:
10.1285/i15900932v18n2p213
Full Text: PDF