IMPROVED CHEN-RICCI INEQUALITY FOR LAGRANGIAN SUBMANIFOLDS IN QUATERNION SPACE FORMS
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- [1] Chen, B.-Y., Relations between Ricci curvature and shape operator for submanifolds with
arbitrary codimensions, Glasgow Math. J. 41 (1999), 33-41.
- [2] Chen, B.-Y., Interaction of Legendre curves and Lagrangian submanifolds, Isreal J. Math.
99 (1997), 69-108.
- [3] Chen,B.-Y., Pseudo-Riemannian geometry, δ invariants and applications, World Scientific,
2011.
- [4] Chen, B.-Y. and Houh, C.-S., Totally real submanifolds of a quaternion projective space,
Ann. Mat. Pura Appl. 120 (1974), 185-199.
- [5] Deng, S., An improved Chen-Ricci Inequality, Int. Electron. J. Geom. 2 (2009), no.2, 39-45.
- [6] Ishihara, S., Quaternion Kahlerian manifolds, J. Diff. Geom.9 (1974), 483-500.
- [7] Liu, X., On Ricci curvature of totally real submanifolds in a quaternion projective space,
Arch Math. (Brno), 38 (2002), 297-305.
- [8] Liu, X. and Dai, W., Ricci curvature of submanifolds in a quaternion projective space, Com-
mun. Korean Math. Soc.17 (2002), No.4, 625-633.
- [9] Oh, Y. M., Lagrangian H-umbilical submanifolds in quaternion Euclidean
spaces,arXiv:math/0311065v1 5 Nov 2003.
- [10] Oprea, T., On a geometric inequality, arXiv:math.DG/0511088v1 3 Nov 2005.
- [11] Oprea, T., Ricci curvature of Lagrangian submanifolds in complex space forms , Math. In-
equal. Appl. 13(2010), no. 4, 851-858.
- [12] Tripathi, M. M., Improved Chen-Ricci inequality for curvature-like tensors and its
application, Differen. Geom. Appl. 29 (2011), no. 5, 685-698.
- [13] Yano, K. and Kon, M., Structures on manifolds, Series in Pure Mathematics, 3. World Sci-
entific Publishing Co., Singapore, 1984.