Conditions for a symmetric connection to be a metric connection

1992 ◽  
Vol 33 (11) ◽  
pp. 3716-3722 ◽  
Author(s):  
S. Brian Edgar
Keyword(s):  
Metric Connection ◽  
Symmetric Connection

scholarly journals Chen-Ricci Inequalities with a Quarter Symmetric Connection in Generalized Space Forms

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Ali H. Al-Khaldi ◽  
Mohd. Aquib ◽  
Mohd Aslam ◽  
Meraj Ali Khan
Keyword(s):  
Complex Space ◽  
Space Form ◽  
Lagrangian Submanifold ◽  
Sasakian Space Form ◽  
Space Forms ◽  
Generalized Complex ◽  
Metric Connection ◽  
Generalized Sasakian Space Form ◽  
Symmetric Connection ◽  
Legendrian Submanifold

In this article, we obtain improved Chen-Ricci inequalities for submanifolds of generalized space forms with quarter-symmetric metric connection, with the help of which we completely characterized the Lagrangian submanifold in generalized complex space form and a Legendrian submanifold in a generalized Sasakian space form. We also discuss some geometric applications of the obtained results.

A note on derived connections from semi-symmetric metric connections

2017 ◽  
Vol 67 (1) ◽  
pp. 221-226
Author(s):  
Adela Mihai
Keyword(s):  
Open Problem ◽  
Complex Structure ◽  
Kaehler Manifold ◽  
Different Types ◽  
Metric Connection

Abstract In this paper we construct examples of different types of connections starting from a semi-symmetric metric connection g, for example a connection which is a symmetric metric connection with respect to a conformally related metric, but symmetric non-metric with respect to the initial metric. We formulate an open problem: to find a parallel complex structure on a Kaehler manifold with respect to such a new connection.

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

Symmetry ◽  
2021 ◽  
Vol 13 (1) ◽  
pp. 79
Author(s):  
Tong Wu ◽  
Yong Wang
Keyword(s):  
Riemannian Manifold ◽  
Metric Connection

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.

Invariant Ricci solitons on three-dimensional metric Lie groups with semi-symmetric connection

2021 ◽  
pp. 80-85
Author(s):  
Pavel Nikolaevich Klepikov ◽  
◽  
Evgeny Dmitrievich Rodionov ◽  
Olesya Pavlovna Khromova ◽  
◽  
...  
Keyword(s):  
Lie Groups ◽  
Three Dimensional ◽  
Ricci Solitons ◽  
Symmetric Connection

Convergence Theory for Unified Discrete-Time RNNs with Quasi-Symmetric Connection

2014 ◽  
Vol 538 ◽  
pp. 167-170
Author(s):  
Hui Zhong Mao ◽  
Chen Qiao ◽  
Wen Feng Jing ◽  
Xi Chen ◽  
Jin Qin Mao
Keyword(s):  
Neural Network ◽  
Global Convergence ◽  
Discrete Time ◽  
Recurrent Neural Network ◽  
Symmetric Matrix ◽  
Network Models ◽  
Convergence Theory ◽  
Connection Matrix ◽  
Neural Network Models ◽  
Symmetric Connection

This paper presents the global convergence theory of the discrete-time uniform pseudo projection anti-monotone network with the quasi–symmetric matrix, which removes the connection matrix constraints. The theory widens the range of applications of the discrete–time uniform pseudo projection anti–monotone network and is valid for many kinds of discrete recurrent neural network models.

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