Bochner formula in generalized (k, μ)-space forms

• Autorzy: B, Shanmukha
• Języki publikacji: EN

Abstrakty

EN

In this article, we studied Green’s theorem and the Bochner formula. Further, we apply the Bochner formula to generalized (k, μ)-space forms and show that the generalized (k, μ) space form is either isometric to a sphere or a certain warped product under some geometric conditions.

Słowa kluczowe

EN

generalized (k, μ) space form; Bochner formula; eigenvalue

• Czasopismo: Journal of Applied Analysis
• Rocznik: 2023
• Tom: Vol. 29, nr 2
• Strony: 323--328
• Opis fizyczny: Bibliogr. 11 poz.

Twórcy

autor

B, Shanmukha

• Department of Mathematics, G. M. Institute of Technology, Davangere, Karnataka, India,

Bibliografia

• [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)-space forms and Da-homothetic deformations, Balkan J. Geom. Appl. 16 (2011), no. 1, 37-47.
• [6] A. Carriazo, V. Martín Molina and M. M. Tripathi, Generalized (κ, μ)-space forms, Mediterr. J. Math. 10 (2013), no. 1, 475-496.
• [7] B.-Y. Chen, Geometry of Submanifolds, Pure Appl. Math. 22, Marcel Dekker, New York, 1973.
• [8] M. Jamali and M. H. Shahid, Application of Bochner formula to generalized Sasakian space forms, Afr. Mat. 29 (2018), no. 7-8, 1135-1139.
• [9] T. Koufogiorgos, Contact Riemannian manifolds with constant ϕ-sectional curvature, Tokyo J. Math. 20 (1997), no. 1, 13-22.
• [10] M. Obata, Certain conditions for a Riemannian manifold to be isometric with a sphere, J. Math. Soc. Japan 14 (1962), 333-340.
• [11] S. Sasaki, On differentiable manifolds with certain structures which are closely related to almost contact structure. I, Tohoku Math. J. (2) 12 (1960), 459-476.

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2024).

Identyfikatory

DOI

10.1515/jaa-2022-1005