A Review on Cartan’s Structure Equations for Certain Classes of Almost Contact Metric Manifolds

Authors

  • Mohammed Y. Abass Department of Mathematics, College of Science, University of Basrah, Basrah, Iraq.

DOI:

https://doi.org/10.56714/bjrs.49.2.1

Keywords:

Kenmotsu manifolds, Cartan’s structure equations, Sasakian manifolds, nearly cosymplectic manifolds

Abstract

This article is review the first group of Cartan’s structure equations for certain classes of almost contact metric manifolds. These classes are divide into two collections, the first involve the irreducible classes such as cosymplectic class, Kenmotsu class, Sasakian class, - class, - class, and - class. The second include normal class of Killing type (CNK-class), nearly Kenmotsu class, - class, - class, nearly cosymplectic class, and Kenmotsu type class

Downloads

Download data is not yet available.

References

V.F. Kirichenko, "Differential-Geometric Structures on Manifolds", Pechatnyy dom, Odessa, (2013). (in Russian)

D. Chinea, C. Gonzalez, Annali di Matematica Pura ed Applicata 156(1), 15 (1990).

Doi: https://doi.org/10.1007/BF01766972

E.S. Volkova, Mathematical Notes 6(3), 296 (1997).

Doi: https://doi.org/10.1007/BF02360870

S.V. Umnova, "Geometry of Kenmotsu manifolds and their generalizations", PhD thesis, Moscow State Pedagogical University, Moscow, (2002). (in Russian).

N.N. Dondukova, "Geodesic transformations of almost contact metric manifolds", PhD thesis, Moscow State Pedagogical University, Moscow, (2006). (in Russian)

A.R. Rustanov, N.N. Shchipkova, Vestnik OSU. (9), 65 (2010). (in Russian)

A.R. Rustanov, N.N. Shchipkova, Vestnik OSU. (1), 132 (2013). (in Russian)

A.R. Rustanov, A.I. Yudin, T.L. Melekhina, Izvestiya Vuzov. Severo-Kavkazskii Region. Natural Science (1), 33 (2019). (in Russian)

Doi: https://doi.org/10.23683/0321-3005-2019-1-33-40

H.İ. Yoldaş, Ş.E. Merİç, E. Yaşar, Miskolc Mathematical Notes 22(2), 1039 (2021).

Doi: https://doi.org/10.18514/MMN.2021.3221

A. Rustanov, Axioms 11, 152 (2022).

Doi: https://doi.org/10.3390/axioms11040152

K. Kenmotsu, Tôhoku Math. J. 24(1), 93 (1972).

Doi: https://doi.org/10.2748/tmj/1178241594

A. De Nicola, G. Dileo, I. Yudin, Annali di Matematica 197(1), 127 (2018).

Doi: https://doi.org/10.1007/s10231-017-0671-2

M.Y. Abass, "Geometry of certain curvature tensors of almost contact metric manifold", PhD thesis, College of Education for Pure Sciences, University of Basrah, (2020).

A. Abu-Saleem, I.D. Kochetkov, A.R. Rustanov, IOP Conference Series: Materials Science and Engineering, Volume 918, VIII International Scientific Conference Transport of Siberia – 2020, 22-27 May 2020, Novosibirsk, Russia, 012062 (2020).

Doi: https://doi.org/10.1088/1757-899X/918/1/012062

A.R. Rustanov, Prepodavatel’ XXI vek (3), 209 (2014). (in Russian)

H.M. Abood, M.Y. Abass, Tamkang J. Math. 52(2), 253 (2021).

Doi: https://doi.org/10.5556/j.tkjm.52.2021.3276

W.M. Boothby, "An introduction to differentiable manifolds and Riemannian geometry", Academic Press, New York, (1975).

V.F. Kirichenko, E.V. Kusova, J. Math. Sci. 177(5), 668 (2011).

Doi: https://doi.org/10.1007/s10958-011-0494-4

V.F. Kirichenko, N.N. Dondukova, Math. Notes 80(2), 204 (2006).

Doi: https://doi.org/10.1007/s11006-006-0129-0

A Review on Cartan’s Structure Equations for Certain Classes of Almost Contact Metric Manifolds

Downloads

Published

30-12-2023

How to Cite

Y. Abass , M. (2023). A Review on Cartan’s Structure Equations for Certain Classes of Almost Contact Metric Manifolds. Basrah Researches Sciences, 49(2), 1–7. https://doi.org/10.56714/bjrs.49.2.1

Issue

Section

Articles