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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J. Berndt, Y. J. Suh, On the geometry of homogeneous real hypersurfaces in the complex quadric, in Proceedings of the 16th International Workshop on Differential Geometry and the 5th KNUGRG-OCAMI Differential Geometry Workshop, vol. 16 (2012), p. 1–9
J. Berndt, Y.J. Suh, Real hypersurfaces with isometric Reeb flow in complex quadric. Int. J. Math. 24, 1350050 (2013)
J.T. Cho, CR-structures on real hypersurfaces of a complex space form. Publ. Math. Debr. 54, 473–487 (1999)
B. Smyth, Differential geometry of complex hypersurfaces. Ann. Math. 85, 246–266 (1967)
Y.J. Suh, Real hypersurfaces in the complex quadric with parallel structure Jacobi operator. Differ. Geom. Appl. 51, 33–48 (2017)
Y.J. Suh, Real hypersurfaces in the complex quadric with commuting and parallel Ricci tensor. J. Geom. Phys. 106, 130–142 (2016)
Y.J. Suh, Real hypersurfaces in the complex quadric with Reeb parallel shape operator. Int. J. Math. 25, 1450059 (2014)
Y.J. Suh, D.H. Hwang, Real hypersurfaces in the complex quadric with commuting Ricci tensor. Sci. China Math. 59, 2185–2198 (2016)
Y.J. Suh, H. Lee, C. Woo, Real hypersurfaces with commuting Jacobi operator in complex quadric. Publ. Math. Debrecen 93, 425–443 (2018)
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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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
- Complex quadric
- Real hypersurface
- Normal Jacobi operator
- Structure Jacobi operator
- Structure tensor
- kth generalized Tanaka–Webster connection
Mathematics Subject Classification