The submanifolds   of the manifold  . II. Fundamental equations on   of

doi:10.1285/i15900932v18n2p227

The submanifolds $Xm$ of the manifold $g-MEXn$ . II. Fundamental equations on $Xm$ of $g-MEXn$

Kiung Tae Chung, Mi Sook. Oh, Jung Mi Ko

Abstract

In our previous paper [4], we studied the induced connection of the $*g-Me$ -connection on a submanifold $Xm$ embedded in a manifold $*g-Mexn$ together with the generalized coefficients $ω_{ij}$ of the second fundamental form of $Xm$ , with emphasis on the proof of a necessary and sufficient condition for the induced connection of $Xm$ in $*g-MEXn$ to be a $*g-ME$ -connection. This paper is a direct continuation of [4]. In this paper, we derive the generalized fundamental equations on $Xm$ of $*g-MEXn$ , 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 $R\mu_{ω\muλ}$ of $*g-MEXn$ and $Rh_{ijk}$ of $Xm$ .

DOI Code: 10.1285/i15900932v18n2p227

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Note di Matematica

The submanifolds $X<sub>m</sub>$ of the manifold $<sup></sup>g-MEX<sub>n</sub>$ . II. Fundamental equations on $X<sub>m</sub>$ of $<sup></sup>g-MEX<sub>n</sub>$

Abstract

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