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>


In our previous paper [4], we studied the induced connection of the <sup>*</sup>g-Me-connection on a submanifold X<sub>m</sub> embedded in a manifold <sup>*</sup>g-Mex<sub>n</sub> together with the generalized coefficients ω_{ij} of the second fundamental form of X<sub>m</sub>, with emphasis on the proof of a necessary and sufficient condition for the induced connection of X<sub>m</sub> in <sup>*</sup>g-MEX<sub>n</sub> to be a <sup>*</sup>g-ME-connection. This paper is a direct continuation of [4]. In this paper, we derive the generalized fundamental equations on X<sub>m</sub> of <sup>*</sup>g-MEX<sub>n</sub>, 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<sup>\mu</sup>_{ω\muλ} of <sup>*</sup>g-MEX<sub>n</sub> and R<sup>h</sup>_{ijk} of X<sub>m</sub>.

DOI Code: 10.1285/i15900932v18n2p227

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