Abstract
In this work, the cases of non-integrable distributions in a Riemannian manifold with the first generalized semi-symmetric non-metric connection and the second generalized semi-symmetric non-metric connection are discussed. We obtain the Gauss, Codazzi, and Ricci equations in both cases. Moreover, Chen’s inequalities are also obtained in both cases. Some new examples based on non-integrable distributions in a Riemannian manifold with generalized semi-symmetric non-metric connections are proposed.
Highlights
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Some properties of a Riemannian manifold endowed with a semi-symmetric metric connection were studied by K
The Gauss, Codazzi, and Ricci equations for distributions are a generalization of the case of submanifolds
Summary
Some properties of a Riemannian manifold endowed with a semi-symmetric metric connection were studied by K. We obtain the Chen inequalities of non-integrable distributions of real-space forms endowed with the first generalized semi-symmetric non-metric connection and the second generalized semisymmetric non-metric connection.
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