Abstract
We have considered a new notion of the shape operator A satisfies Killing tensor type for real hypersurfaces M in complex Grassmannians of rank two. With this notion we prove the non-existence of real hypersurfaces M in complex Grassmannians of rank two.
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References
Alekseevskii, D.V.: Compact quaternion spaces. Func. Anal. Appl. 2, 106–114 (1966)
Blair, D.E.: Riemannian geometry of contact and symplectic manifolds. Springer Science and Business Media (2010)
Jeong, I., Machado, C., Pérez, J.D., Suh, Y.J.: Real hypersurfaces in complex two-plane Grassmannians with \({\cal{D}}^{\bot }\)-parallel structure Jacobi operator. Int. J. Math. 22(5), 655–673 (2011)
Lee, H., Choi, Y.S., Woo, C.: Hopf hypersurfaces in complex two-plane Grassmannians with Reeb parallel shape operator. Bull. Malaysian Math. Soc. 38(3), 617–634 (2015)
Lee, H., Suh, Y.J.: Real hypersurfaces of type \(B\) in complex two-plane Grassmannians related to the Reeb vector. Bull. Korean Math. Soc. 47(3), 551–561 (2010)
Lee, H., Suh, Y.J., Woo, C.: Real hypersurfaces with commuting Jacobi operators in complex two-plane Grassmannians. Houston J. Math. 40(3), 751–766 (2014)
Pérez, J.D., Suh, Y.J.: The Ricci tensor of real hypersurfaces in complex two-plane Grassmannians. J. Korean Math. Soc. 44, 211–235 (2007)
Pérez, J.D., Suh, Y.J., Woo, C.: Real hypersurfaces in complex two-plane Grassmannians with GTW Harmonic curvature. Canad. Math. Bull. 58(4), 835–845 (2015)
Pérez, J.D., Suh, Y.J., Woo, C.: Real hypersurfaces in complex two-plane Grassmannians whose shape operator is recurrent for the generalized Tanaka-Webster connection. Turkish J. Math. 39(3), 313–321 (2015)
Pérez, J.D., Suh, Y.J., Woo, C.: Real Hypersurfaces in complex hyperbolic two-plane Grassmannians with commuting shape operator. Open Math. 13(1), 493–501 (2015)
Suh, Y.J.: Real hypersurfaces in complex two-plane Grassmannians with parallel shape operator. Bull. Austral. Math. Soc. 68, 493–502 (2003)
Suh, Y.J.: Real hypersurfaces in complex two-plane Grassmannians with parallel shape operator II. J. Korean Math. Soc. 41, 535–565 (2004)
Suh, Y.J.: Real hypersurfaces in complex two-plane Grassmannians with parallel Ricci tensor. Proc. Royal Soc. Edinb. A. 142, 1309–1324 (2012)
Suh, Y.J.: Hypersurfaces with isometric Reeb flow in complex hyperbolic two-plane Grassmannians. Adv. Appl. Math. 50, 645–659 (2013)
Suh, Y.J.: Real hypersurfaces in complex two-plane Grassmannians with harmonic curvature. J. Math. Pures Appl. 100, 16–33 (2013)
Suh, Y.J.: Real hypersurfaces in complex hyperbolic two-plane Grassmannians with Reeb vector field. Adv. Appl. Math. 55, 131–145 (2014)
Suh, Y.J.: Real hypersurfaces in complex hyperbolic two-plane Grassmannians with commuting Ricci tensor. Int. J. Math., World Sci. Publ. 26, 1550008 (26 pages) (2015)
Suh, Y.J., Woo, C.: Real Hypersurfaces in complex hyperbolic two-plane Grassmannians with parallel Ricci tensor. Math. Nachr. 287, 1524–1529 (2014)
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Jang, JE., Suh, Y.J., Woo, C. (2017). Real Hypersurfaces in Hermitian Symmetric Space of Rank Two with Killing Shape Operator. In: Suh, Y., Ohnita, Y., Zhou, J., Kim, B., Lee, H. (eds) Hermitian–Grassmannian Submanifolds. Springer Proceedings in Mathematics & Statistics, vol 203. Springer, Singapore. https://doi.org/10.1007/978-981-10-5556-0_23
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DOI: https://doi.org/10.1007/978-981-10-5556-0_23
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