JOURNAL BROWSE
Search
Advanced SearchSearch Tips
Real Hypersurfaces in Complex Two-plane Grassmannians with F-parallel Normal Jacobi Operator
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
  • Journal title : Kyungpook mathematical journal
  • Volume 51, Issue 4,  2011, pp.395-410
  • Publisher : Department of Mathematics, Kyungpook National University
  • DOI : 10.5666/KMJ.2011.51.4.395
 Title & Authors
Real Hypersurfaces in Complex Two-plane Grassmannians with F-parallel Normal Jacobi Operator
Jeong, Im-Soon; Suh, Young-Jin;
  PDF(new window)
 Abstract
In this paper we give a non-existence theorem for Hopf hypersurfaces M in complex two-plane Grassmannians whose normal Jacobi operator is parallel on the distribution F defined by , where [] = Span{}, = Span {, , } and , .
 Keywords
Real hypersurfaces;Complex two-plane Grassmannians;F-parallel normal Jacobi operator;Hopf hypersurfaces;
 Language
English
 Cited by
1.
Commuting structure Jacobi operator for real hypersurfaces in complex two-plane Grassmannians, Acta Mathematica Sinica, English Series, 2015, 31, 1, 111  crossref(new windwow)
2.
Semi-parallelism of normal Jacobi operator for Hopf hypersurfaces in complex two-plane Grassmannians, Monatshefte für Mathematik, 2013, 172, 2, 167  crossref(new windwow)
3.
Characterizations for Real Hypersurfaces in Complex and Quaternionic Space Forms Related to the Normal Jacobi Operator, Kyungpook mathematical journal, 2016, 56, 3, 993  crossref(new windwow)
4.
Generalized Tanaka-Webster and Levi-Civita connections for normal Jacobi operator in complex two-plane Grassmannians, Czechoslovak Mathematical Journal, 2015, 65, 2, 569  crossref(new windwow)
5.
Hopf hypersurfaces in complex two-plane Grassmannians with generalized Tanaka-Webster parallel normal Jacobi operator, Czechoslovak Mathematical Journal, 2015, 65, 1, 207  crossref(new windwow)
 References
1.
D. V. Alekseevskii, Compact quaternion spaces, Func. Anal. Appl., 2(1968), 106-114. crossref(new window)

2.
J. Berndt, Real hypersurfaces in quaternionic space forms, J. Reine Angew. Math., 419(1991), 9-26.

3.
J. Berndt and Y. J. Suh, Real hypersurfaces in complex two-plane Grassmannians, Monatshefte fur Math., 127(1999), 1-14. crossref(new window)

4.
J. Berndt and Y. J. Suh, Isometric ows on real hypersurfaces in complex two-plane Grassmannians, Monatshefte fur Math., 137(2002), 87-98. crossref(new window)

5.
I. Jeong, J. D. Perez and Y. J. Suh Real hypersurfaces in complex two-plane Grassmannians with commuting normal Jacobi operator, Acta Math. Hungarica, 117(2007), 201-217. crossref(new window)

6.
I. Jeong and Y. J. Suh Real hypersurfaces in complex two-plane Grassmannians with Lie $\xi$-parallel normal Jacobi operator, J. of Korean Math. Soc., 45(2008), 1113-1133. crossref(new window)

7.
I. Jeong, H. J. Kim and Y. J. Suh Real hypersurfaces in complex two-plane Grassmannians with parallel normal Jacobi operator, Publ. Math. Debrecen, 76(2010), 203-218.

8.
U-H. Ki, J. D. Perez, F. G. Santos and Y. J. Suh Real hypersurfaces in complex space forms with $\xi$-parallel Ricci tensor and structure Jacobi operator, J. of Korean Math. Soc., 44(2007), 307-326. crossref(new window)

9.
U-H. Ki and Y. J. Suh, Real hypersurfaces in complex hyperbolic space with commuting Ricci tensor, Kyungpook Math. J., 48(2008), 433-442. crossref(new window)

10.
M. Kimura, Real hypersurfaces and complex submanifolds in complex projective space, Trans. Amer. Math. Soc., 296(1986), 137-149. crossref(new window)

11.
J. D. Perez and Y. J. Suh, Real hypersurfaces of quaternionic projective space satisfying ${\nabla}_U_{\iota}R$= 0, Diff. Geom. and Its Appl., 7(1997), 211-217. crossref(new window)

12.
J. D. Perez and Y. J. Suh, The Ricci tensor of real hypersurfaces in complex two-plane Grassmannians, J. of Korean Math. Soc., 44(2007), 211-235. crossref(new window)

13.
J. D. Perez, F. G. Santos and Y. J. Suh, Real hypersurfaces in complex projective space whose structure Jacobi operator is Lie $\xi$-parallel, Diff. Geom. and Its Appl., 22(2005), 181-188. crossref(new window)

14.
Y. J. Suh, Real hypersurfaces in complex two-plane Grassmannians with parallel shape operator, Bull. of Austral. Math. Soc., 67(2003), 493-502. crossref(new window)

15.
Y. J. Suh, Real hypersurfaces in complex two-plane Grassmannians with parallel shape operator II, J. of Korean Math. Soc., 41(2004), 535-565. crossref(new window)

16.
Y. J. Suh, Real hypersurfaces in complex two-plane Grassmannians with vanishing Lie derivatives, Canadian Math. Bull., 49(2006), 134-143. crossref(new window)

17.
Y. J. Suh, Real hypersurfaces of type B in complex two-plane Grassmannians, Monatshefte fur Math., 147(2006), 337-355. crossref(new window)