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RICCI CURVATURE OF INTEGRAL SUBMANIFOLDS OF AN S-SPACE FORM
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 Title & Authors
RICCI CURVATURE OF INTEGRAL SUBMANIFOLDS OF AN S-SPACE FORM
Kim, Jeong-Sik; Dwivedi, Mohit Kumar; Tripathi, Mukut Mani;
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 Abstract
Involving the Ricci curvature and the squared mean curvature, we obtain a basic inequality for an integral submanifold of an S-space form. By polarization, we get a basic inequality for Ricci tensor also. Equality cases are also discussed. By giving a very simple proof we show that if an integral submanifold of maximum dimension of an S-space form satisfies the equality case, then it must be minimal. These results are applied to get corresponding results for C-totally real submanifolds of a Sasakian space form and for totally real submanifolds of a complex space form.
 Keywords
S-space form;integral submanifold;C-totally real submanifold;totally real submanifold;Lagrangian submanifold;Ricci curvature;k-Ricci curvature;scalar curvature;
 Language
English
 Cited by
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 References
1.
D. E. Blair, Geometry of manifolds with structural group $U(n){\times}O(s)$, J. Diff. Geometry 4 (1970), 155-167

2.
D. E. Blair, On a generalization of the Hopf fibration, An. Sti. Univ. 'Al. I. Cuza' Iasi Sect. I a Mat. (N.S.) 17 (1971), 171-177

3.
D. E. Blair, Riemannian geometry of contact and symplectic manifolds, Progress in Mathematics, 203. Birkhauser Boston, Inc., Boston, MA, 2002

4.
D. E. Blair, G. D. Ludden, and K. Yano, Differential geometric structures on principal toroidal bundles, Trans. Amer. Math. Soc. 181 (1973), 175-184 crossref(new window)

5.
J. L. Cabrerizo, L. M. Fernandez, and M. Fernandez, The curvature of submanifolds of an S-space form, Acta Math. Hungar. 62 (1993), no. 3-4, 373-383 crossref(new window)

6.
J. L. Cabrerizo, L. M. Fernandez, and M. Fernandez, On certain anti-invariant submanifolds of an S-manifold, Portugal. Math. 50 (1993), no. 1, 103-113

7.
B.-Y. Chen, Relations between Ricci curvature and shape operator for submanifolds with arbitrary codimensions, Glasg. Math. J. 41 (1999), no. 1, 33-41 crossref(new window)

8.
B.-Y. Chen, On Ricci curvature of isotropic and Langrangian submanifolds in complex space forms, Arch. Math. (Basel) 74 (2000), no. 2, 154-160 crossref(new window)

9.
S. P. Hong and M. M. Tripathi, On Ricci curvature of submanifolds, Int. J. Pure Appl. Math. Sci. 2 (2005), no. 2, 227-245

10.
X. Liu, On Ricci curvature of C-totally real submanifolds in Sasakian space forms, Acta Math. Acad. Paedagog. Nyhazi. (N.S.) 17 (2001), no. 3, 171-177

11.
K. Matsumoto, I. Mihai, Ricci tensor of C-totally real submanifolds in Sasakian space forms, Nihonkai Math. J. 13 (2002), no. 2, 191-198

12.
I. Mihai, Ricci curvature of submanifolds in Sasakian space forms, J. Aust. Math. Soc. 72 (2002), no. 2, 247-256 crossref(new window)

13.
H. Nakagawa, On framed f-manifolds, Kodai Math. Sem. Rep. 18 (1966) 293-306 crossref(new window)

14.
D. Van Lindt, P. Verheyen, and L. Verstraelen, Minimal submanifolds in Sasakian space forms, J. Geom. 27 (1986), no. 2, 180-187 crossref(new window)

15.
J. Van.zura, Almost r-contact structures, Ann. Scuola Norm. Sup. Pisa (3) 26 (1972), 97-115

16.
S. Yamaguchi, M. Kon, and T. Ikawa, C-totally real submanifolds, J. Differential Geometry 11 (1976), no. 1, 59-64

17.
K. Yano and M. Kon, Structures on manifolds, Series in Pure Mathematics, 3. World Scientific Publishing Co., Singapore, 1984