Open Access
Article
Optimal Inequalities for Generalized Normalized δ-Casorati Curvatures for Hi-Slant Submanifolds of Kenmotsu Space Forms
- Received:
- 22 Oct 2017
- Accepted:
- 19 Mar 2018
- Published Online:
- 16 May 2019
- Article type:
- Article
- Language:
- EN
- Article no.:
- 1726037X.2018.1564579
- Pages:
- 39–50
Abstract
The main objective of the present paper is to generalize the inequalities obtained by the same author M. A. Lone, Filomat, 31:15, pp 4925-4932 and M.A. Lone, Balkan Journal of Geometry and Its Applications, 22(1), pp 41-50 in the contact version. We consider hi-slant submanifolds of Kenmotsu space forms to obtain the inequalities and also discuss the equality case.
Keywords
Subject Classifications
53B0553B2053C40
References
- D.Blair, Contact manifolds in Riemannian Geometry, Lectures Notes in Math . 509, Springer-Verlag , Berlin, 1976 .
- D.Blair and A.Ledger, Quasi-umbilical, minimal submanifolds of of Euclidean space , Simon Stevin , Vol. 51 , 3 - 22 ( 1977 ).
- F.Casorati, Mesure de la courbure des surface suivant 1’idee commune. Ses rapports avec les mesures de coubure gaussienne et moyenne , Acta Math ., Vol. 14 , 95 - 110 ( 1999 ).
- A.Carriazo, Bi-slant immersions. Proceedings of ICRAMS, Kharagpur 88-97, 2000 .
- B.Y.Chen, Pseudo-Riemannian Geometry, -Invariants and Applications , World Scientic , New Jersey, 2011 .
- S.Decu S, S.Haesen and L.Verstralelen, Optimal inequalities involving Casorati curvatures , Bull. Transylv. Univ. Brasov, Ser B , Vol. 49 , 85 - 93 ( 2007 ).
- S.Decu S, S.Haesen and L.Verstralelen, Optimal inequalities characterizing quasi-umbilical submanifolds , J. Inequalities Pure. Appl. Math , 9 , 2008 , Article ID 79, 7pp .
- V.Ghisoiu, Inequalities for thr Casorati curvatures of the slant submanifolds in complex space forms, Riemannian geometry and applications. Proceedings RIGA 2011, ed. Univ. Bucuresti, Bucharest, 2011, 145-150 .
- S.Haesen, D.Kowalczyk and L.Verstralelen, On the extrinsic principal directions of Riemannnian submanifolds , Note Math ., Vol. 29 , 41 - 53 ( 2009 ).
- K.Kenmotsu, A class of almost contact Riemannian manifolds , Tohoku Math. J . Vol. 24 , Number 2 , 93 - 103 ( 1972 ).
- D.Kowalczyk, Casorati curvatures, Bull. Transilvania Univ. Brasov Ser. III, Vol. 50, Number 1, 2009-2013(2008) .
- C.W.Lee, J. W.Lee and G.E.Vilcu, Optimal inequalities for the normalized -Casorati curvatures of submanifolds in Kenmotsu space forms , Adv. in Geom ., Vol. 17 , Number 3 , 355 - 362 ( 2017 ).
- C.W.Lee, D.W.Yoon and J.W.Lee, Optimal inequalities for the Casorati curvatures of submanifolds of real space forms endowed with semi-symmetric metric connections , J. Inequal. Appl ., 9 pp. MR3344114(2014) .
- C.W.Lee, J.W.Lee, G.E.Vilcu and D.W.Yoon, Optimal inequalities for the Casorati curvatures of the submanifolds of Generalized space form endowed with seni-symmetric metric connections , Bull. Korean Math. Soc . Vol. 52 , 1631 - 1647 ( 2015 ).
- J.W.Lee and G.E.Vilcu, Inequalities for generalized normalized -Casorati curvatures of slant submanifolds in quaternion space forms , Taiwanese J. Math ., 19 , 691 - 702 ( 2015 ).
- A.Lotta, Slant submanifolds in contact geometry , Bull. Math. Soc. Roumanie ,Vol. 39 , 183 - 198 ( 1996 ).
- M.A.Lone, An inequality for generalized normalized -Casorati curvatures of slant submanifolds in generalized complex space form , Balkan Journal of Geometry and Its Applications , 22 ( 1 ), 41 - 50 ( 2017 ).
- M.A.Lone, A lower bound of normalized scalar curvature for the submanifolds of locally conformal Kaehler space form using Casorati curvatures , Filomat , 31 ( 15 ), 4925 - 4932 , ( 2017 ).
- M.M.Tripathi, Inequalities for algebraic Casorati curvatures and their applications , arXiv : 1607.05828v1 [math.DG] 20 Jul 2016 .
- L.Verstralelen, Geometry of submanifolds I, The first Casorati curvature indicatrices , Kragujevac J. Math ., Vol. 37 , 5 - 23 ( 2013 ).
- L.Verstralelen, The geometry of eye and brain , Soochow J. Math ., Vol. 30 , 367 - 376 ( 2004 ).
Views: 26Downloads: 50Citations: 0
