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.

中文翻译：

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不可积分布的广义半对称非度量连接

在这项工作中，讨论了具有第一广义半对称非度量连接和第二广义半对称非度量连接的黎曼流形中的不可积分分布的情况。在这两种情况下，我们都获得了高斯，科达兹​​和里奇方程。此外，在两种情况下都可以得到陈氏不等式。提出了一些基于广义半对称非度量连接的黎曼流形中不可积分布的新例子。