Generalized Semi-Symmetric Non-Metric Connections of Non-Integrable Distributions

Wu, Tong; Wang, Yong

doi:10.3390/sym13010079

Open AccessArticle

Generalized Semi-Symmetric Non-Metric Connections of Non-Integrable Distributions

by

Tong Wu

and

Yong Wang

^*

School of Mathematics and Statistics, Northeast Normal University, Changchun 130024, China

^*

Author to whom correspondence should be addressed.

Symmetry 2021, 13(1), 79; https://doi.org/10.3390/sym13010079

Submission received: 16 December 2020 / Revised: 30 December 2020 / Accepted: 2 January 2021 / Published: 5 January 2021

(This article belongs to the Section B: Mathematics)

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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.

Keywords: non-integrable distributions; semi-symmetric non-metric connections; Chen’s inequalities; Einstein distributions; distributions with constant scalar curvature

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MDPI and ACS Style

Wu, T.; Wang, Y. Generalized Semi-Symmetric Non-Metric Connections of Non-Integrable Distributions. Symmetry 2021, 13, 79. https://doi.org/10.3390/sym13010079

AMA Style

Wu T, Wang Y. Generalized Semi-Symmetric Non-Metric Connections of Non-Integrable Distributions. Symmetry. 2021; 13(1):79. https://doi.org/10.3390/sym13010079

Chicago/Turabian Style

Wu, Tong, and Yong Wang. 2021. "Generalized Semi-Symmetric Non-Metric Connections of Non-Integrable Distributions" Symmetry 13, no. 1: 79. https://doi.org/10.3390/sym13010079

APA Style

Wu, T., & Wang, Y. (2021). Generalized Semi-Symmetric Non-Metric Connections of Non-Integrable Distributions. Symmetry, 13(1), 79. https://doi.org/10.3390/sym13010079

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Generalized Semi-Symmetric Non-Metric Connections of Non-Integrable Distributions

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