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Classification of real hypersurfaces in complex quadric in terms of new tensors

Abstract

In this paper two new tensor fields on real hypersurfaces in complex quadric are introduced. Real hypersurfaces on which the derivatives of the tensor fields with respect to the Levi-Civita connection and the k-th generalized Tanaka–Webster connection of them coincide are studied leading to new classification results on real hypersurfaces in a complex quadric.

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Acknowledgements

The third author is supported by MINECO-FEDER Project MTM 2016-78807-C2-1-P.

The authors would like to thank the reviewers for their valuable comments which improved the paper.

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Correspondence to George Kaimakamis.

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Kaimakamis, G., Panagiotidou, K. & Pérez, J.d.D. Classification of real hypersurfaces in complex quadric in terms of new tensors. Period Math Hung (2021). https://doi.org/10.1007/s10998-021-00383-0

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Keywords

  • Complex quadric
  • Real hypersurface
  • Normal Jacobi operator
  • Structure Jacobi operator
  • Structure tensor
  • kth generalized Tanaka–Webster connection

Mathematics Subject Classification

  • 53C15
  • 53B25