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Some new results on real hypersurfaces with generalized Tanaka-Webster connection

  • Wenjie Wang EMAIL logo and Ximin Liu
Published/Copyright: May 21, 2019
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Abstract

Let M be a real hypersurface in nonflat complex space forms of complex dimension two. In this paper, we prove that the shape operator of M is transversally Killing with respect to the generalized Tanaka-Webster connection if and only if M is locally congruent to a type (A) or (B) real hypersurface. We also prove that shape operator of M commutes with Cho operator on holomorphic distribution if and only if M is locally congruent to a ruled real hypersurface.


This work was supported by the National Natural Science Foundation of China (No. 11431009).


  1. (Communicated by Július Korbaš)

Acknowledgement

The authors would like to thank the referee for many useful comments which improves the original paper.

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Received: 2018-05-14
Accepted: 2018-10-21
Published Online: 2019-05-21
Published in Print: 2019-06-26

© 2019 Mathematical Institute Slovak Academy of Sciences

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