Generalized Killing structure Jacobi operator for real hypersurfaces in complex hyperbolic two-plane Grassmannians

다국어 초록 (Multilingual Abstract)

In this paper, first we introduce a new notion of generalized Killing structure Jacobi operator for a real hypersurface $M$ in complex hyperbolic two-plane Grassmannians $S U_{2, m} / S\left(U_{2} \cdot U_{m}\right)$. Next we prove that there does not exist a Hopf real hypersurface in complex hyperbolic two-plane Grassmannians $S U_{2, m} / S\left(U_{2} \cdot U_{m}\right)$ with generalized Killing structure Jacobi operator.

참고문헌 (Reference)

1 Juan de Dios P\'erez ; 서영진, "The Ricci tensor of real hypersurfaces in complex two-plane Grassmannians" 대한수학회 44 (44): 211-235, 2007

2 H. Lee, "Reeb parallel Ricci tensor for homogeneous real hypersurfaces in complex hyperbolic two-plane Grassmannians" 288 : 1-12, 2015

3 J. Berndt, "Real hypersurfaces with isometric Reeb flow in Kähler manifolds" 23 (23): 1950039-, 2021

4 J. D. Pérez, "Real hypersurfaces of quaternionic projective space satisfying ∇UiR = 0" 7 (7): 211-217, 1997

5 A. Martínez, "Real hypersurfaces in quaternionic projective space" 145 : 355-384, 1986

6 J. Berndt, "Real hypersurfaces in hermitian symmetric spaces, Advances in Analysis and Geometry" Walter de Gruyter GmbH

7 H. Lee, "Real hypersurfaces in complex two-plane Grassmannians with certain commuting condition II" 64 (64): 133-148, 2014

8 I. Jeong, "Real hypersurfaces in complex two-plane Grassmannians with D⊥-parallel structure Jacobi operator" 22 (22): 655-673, 2011

9 H. Lee, "Real hypersurfaces in complex hyperbolic two-plane Grassmannians with commuting structure Jacobi operators" 13 (13): 3389-3407, 2016

10 Y. J. Suh, "Real hypersurfaces in complex hyperbolic two-plane Grassmannians with commuting Ricci tensor" 26 (26): 1550008-, 2015

11 Y. J. Suh, "Real hypersurfaces in complex hyperbolic two-plane Grassmannians with Reeb vector field" 55 : 131-145, 2014

12 Y. J. Suh, "Real hypersurfaces in complex hyperbolic two-plane Grass-mannians with parallel Ricci tensor" 287 (287): 1524-1529, 2014

13 H. Lee, "Quadratic Killing structure Jacobi operator for real hypersurfaces in complex two-plane Grassmannians"

14 H. Lee, "Quadratic Killing normal Jacobi operator for real hypersurfaces in complex Grassmannians of rank 2" 160 : 103975-, 2021

15 K. Yano, "On harmonic and Killing vector fields" 55 : 38-45, 1952

16 A. Borel, "Les sous-groupes fermés de rang maximum des groupes de Lie clos" 23 : 200-221, 1949

17 W. Ballmann, "Lectures on Kähler manifolds, ESI Lectures in Mathematics and Physics" European Mathematical Society 2006

18 J. F. Adams, "Lectures on Exceptional Lie Groups, Chicago Lectures in Mathematics" University of Chicago Press 1996

19 G. Thompson, "Killing tensors in spaces of constant curvature" 27 (27): 2693-2699, 1986

20 K. Heil, "Killing and conformal Killing tensors" 106 : 383-400, 2016

21 Y. J. Suh, "Hypersurfaces with isometric Reeb flow in complex hyperbolic two-plane Grassmannians" 50 (50): 645-659, 2013

22 J. Berndt, "Hypersurfaces in noncompact complex Grassmannians of rank two" 23 (23): 1250103-, 2012

23 R. -H. Lee, "Hopf hypersurfaces in complex Grassmannians of rank two" 71 (71): 1083-1107, 2017

24 K. Yano, "Harmonic and Killing vector fields in compact orientable Riemannian spaces with boundary" 69 : 588-597, 1959

25 K. Yano, "Harmonic and Killing tensor fields in Riemannian spaces with boundary" 10 : 430-437, 1958

26 Y. J. Suh, "Generalized Killing-Ricci tensor for real hypersurfaces in complex hyperbolic two-plane Grassmannians" 18 (18): 28-, 2021

27 Y. J. Suh, "Generalized Killing Ricci tensor for real hypersurfaces in complex two-plane Grassmannians" 159 : 103799-, 2021

28 J. D. Pérez, "Generalized Einstein real hypersurfaces in complex two-plane Grassmannians" 60 (60): 1806-1818, 2010

29 S. Helgason, "Differential geometry, Lie groups, and symmetric spaces" American Mathematical Society 2001

30 J. D. Pérez, "Cyclic-parallel real hypersurfaces of quaternionic projective space" 17 (17): 189-191, 1993

31 J. Berndt, "Contact hypersurfaces in Kähler manifolds" 143 (143): 2637-2649, 2015

32 U. Semmelmann, "Conformal Killing forms on Riemannian manifolds" 245 (245): 503-527, 2003

33 J. D. Pérez, "Comparing Lie derivatives on real hypersurfaces in complex projective spaces" 13 (13): 2161-2169, 2016

34 D. E. Blair, "Almost contact manifolds with Killing structure tensors" 39 : 285-292, 1971