Affiliation:
1. Department of Mathematics , G. M. Institute of Technology , Davangere , Karnataka , India
Abstract
Abstract
In this article, we studied Green’s theorem and the Bochner formula. Further, we apply the Bochner formula to generalized
(
k
,
μ
)
{(k,\mu)}
-space forms and show that the generalized
(
k
,
μ
)
{(k,\mu)}
space form is either isometric to a sphere or a certain warped product under some geometric conditions.
Subject
Applied Mathematics,Computational Theory and Mathematics,Statistics, Probability and Uncertainty,Mathematical Physics
Reference11 articles.
1. P. Alegre, D. E. Blair and A. Carriazo,
Generalized Sasakian-space-forms,
Israel J. Math. 141 (2004), 157–183.
2. P. Alegre and A. Carriazo,
Structures on generalized Sasakian-space-forms,
Differential Geom. Appl. 26 (2008), no. 6, 656–666.
3. A. Barros,
Applications of Bochner formula to minimal submanifold of the sphere,
J. Geom. Phys. 44 (2002), no. 2–3, 196–201.
4. D. E. Blair,
Contact Manifolds in Riemannian Geometry,
Lecture Notes in Math. 509,
Springer, Berlin, 1976.
5. A. Carriazo and V. Martín-Molina,
Generalized
(
κ
,
μ
)
{(\kappa,\mu)}
-space forms and
D
a
{D_{a}}
-homothetic deformations,
Balkan J. Geom. Appl. 16 (2011), no. 1, 37–47.