Generalized Kenmotsu manifold constancy of type
https://doi.org/10.22405/2226-8383-2019-20-2-7-21
Abstract
In this work we consider generalized Kenmotsu manifolds, we introduce: the fourth and
the fifth fundamental identities of generalized Kenmotsu manifolds; the first and the second
structural tensors of generalized Kenmotsu manifolds (and we prove their properties); the
concept of adjoint Q-algebra for generalized Kenmotsu manifolds. We prove that generalized
Kenmotsu manifolds and the II kind special generalized Kenmotsu manifolds have
anticommutative adjoint Q-algebra. And the Kenmotsu manifolds and the I kind special
generalized Kenmotsu manifolds have Abelian adjoint Q-algebra. The type constancy contact
analog is introduced and the constant-type generalized Kenmotsu manifolds are thoroughly
examined. We have identified the type point constancy conditions of the generalized Kenmotsu
manifolds in the adjoint G-structure space. We prove that the zero constant type GKmanifold
class coincides with the Kenmotsu manifold class and the non-zero constant type
GK-manifold class can be concircularly transformed into the almost contact metric manifolds
locally equivalent to the product of the six dimensional NK-eigenmanifold and the real straight
line.
About the Authors
Ahmad Abu-SaleemJordan
Aligadzhi Rabadanovich Rustanov
Russian Federation
Tatyana Leonidovna Melekhina
Russian Federation
References
1. Kirichenko, V. F., 1981, “Almost Hermitian manifolds of the constant type”, Report. ASUSSR, vol. 256, no. 16, pp. 1293–1297.
2. Gray, A., 1976, “Curvature identities for Hermitian and almost Hermitian manifolds”, Tôhoku Math. J., vol. 28, pp. 601–612.
3. Kirichenko, V. F. 1976, “Constant type K-spaces”, Sib. Math. J., vol. 17, no. 12, pp. 282–289.
4. Umnova, S. V., 2002, “On conformal invariants of Kenmotsu manifolds”, Webs and Quasigroups, Tver State Univ., pp. 155–160.
5. Kenmotsy, K., 1972, “A class of almost contact Riemannian manifolds”, Tôhoku Math. J., vol. 24, pp. 93–103.
6. Blair, D. E., Showders, D. K., 1974, “Almost contact manifolds with Killing structure tensors”, J. Differential Geom., vol. 9, pp. 577–582.
7. Kirichenko, V. F., 2013, Differential geometric structures on manifolds, Petchatny Dom, Odessa, 458 p.
8. Kirichenko, V. F., Rustanov, A. R., 2002, “Quasi-Sasakian manifolds differential” , Mathematical collection, vol. 193(18), pp. 71–100.
9. Abu-Saleem Ahmad, Rustanov, A. R., 2018, “Some aspects geometry of generalized manifolds Kenmotsu”, Far East Journal of Mathematical Sciences (FJMS), vol. 103, no. 9, pp. 1407–1432.
10. Abu-Saleem, A., Rustanov, A. R., Kharitonova S. V., 2018, “Generalized Kenmotsu manifold integrability properties”, Vladikavkasian Mathematical Journal, vol. 20(3), pp. 4–20. DOI 10.23671/VNC.2018.3.13829.
11. Kirichenko, V. F.,1994, “Generalized quasi-Kaehlerian manifolds and axioms of CR-submanifolds in generalized Hermitian geometry”, Geom. Dedicata, vol. 51. pp. 75–104.
12. Arsenyeva, O. E., Kirichenko, V. F., 2013, “Q-algebras of the main types of almost Hermitian and almost contact metrical manifolds”, Proc. Intern. Geom. Center, vol. 6, no. 4, pp. 34–43.
13. Kirichenko, V. F., 1981, “Holomorphic plane axiom in generalized Hermitian geometry”, ASUSSR reports, vol. 260(14), pp. 795–799.
14. Kirichenko, V. F., 1981, “K-algebras and K-spaces of the constant type with indefinite metrics”, Math. notes, vol. 29(12), pp. 265–278.
15. Abu-Saleem, A., Rustanov, A. R., 2015, “Curvature Identities Special Generalized Manifolds Kenmotsu Second Kind”, Malaysian Journal of Mathematical Sciences, vol. 9(12), pp. 187–207.
Review
For citations:
Abu-Saleem A., Rustanov A.R., Melekhina T.L. Generalized Kenmotsu manifold constancy of type. Chebyshevskii Sbornik. 2019;20(2):7-21. https://doi.org/10.22405/2226-8383-2019-20-2-7-21
Views:
581
Email this article 