Generalized Wintgen inequality for submanifolds in Kenmotsu space forms

Main Article Content

Mohd Aquib
Mohammad Hasan Shahid

Abstract

In this paper, we obtain the generalized Wintgen inequality for Legendrian submanifolds in Kenmotsu space forms and discuss the equality case of the inequality. Further, we discuss the inequality for bi-slant submanifold in the same ambient space and derive its application in various slant cases.

Article Details

How to Cite
Aquib, M., & Shahid, M. H. (2021). Generalized Wintgen inequality for submanifolds in Kenmotsu space forms. Tamkang Journal of Mathematics, 50(2), 155–164. https://doi.org/10.5556/j.tkjm.50.2019.2845
Section
Papers
Author Biographies

Mohd Aquib, Jamia Millia Islamia University

Department ofMathematics, Faculty of Natural Sciences, JamiaMillia Islamia, New Delhi-110025, India.

Mohammad Hasan Shahid, Jamia Millia Islamia University

Department ofMathematics, Faculty of Natural Sciences, JamiaMillia Islamia, New Delhi-110025, India.

References

K. Arslan, I.Mihai, C.Murathan and C. Ozgur, Ricci curvature of submanifolds in Kenmotsu space forms, Int.

J.Math.Math. Sci., 29 (2002), 719–726.

M. N. Boyom, M. Aquib, M. H. Shahid and M. Jamali, Generalized wintegen type inequality for lagrangian

submanifolds in holomorphic statistical space forms, In: Nielsen F., Barbaresco F. (eds) Geometric Science of

Information, GSI 2017, Lecture Notes in Computer Science, Springer, Cham10589.

J. Ge and Z. Tang, A proof of the DDVV conjecture and its equality case, Pacific J.Math., 237(2009), (1), 87–95.

I. V. Guadalupe and L. Rodriguez, Normal curvature of surfaces in space forms, Pacific J. Math., 106 (1983),

–103.

S. Haesen and L. Verstraelen, Natural Intrinsic Geometrical Symmetries, Symmetry, Integrability and Geometry:Methods and Applications, 5 (2009), paper 086, pp. 15.

K. Kenmotsu, A class of almost contact Riemannianmanifolds, TohokuMath. J., 24 (1972), 93–103.

C.W. Lee, J.W. Lee and G. E. Vilcu, Optimal inequalities for the normalized ±-Casorati curvatures of submanifolds

in Kenmotsu space forms, Adv. Geom., 17(2017), 355–362.

Z. Lu, Normal scalar curvature conjecture and its applications, J. fucnt. Analysis, 261 (2011), 1284–1308.

I.Mihai, On the generalizedWintgen inequality for lagrangian submanifolds in complex space form, Nonlinear

Analysis, 95 (2014), 714–720.

C. Murathan, K. Arslan, R. Ezentas and I. Mihai, Warped product submanifolds in Kenmotsu space forms,

Taiwanese. J.Math., 10(2006), 1431–1441.

P.Wintgen, Sur l’inégalité de Chen-Wilmore, C. R. Acad. Sci. Paris Ser. A-B, 288 (1979), A993–A995.

K. Yano andM. Kon, Anti-invariant Submanifolds,M. Dekker, New York, 1976.