Concircularly and Conharmonically Flat Warped-Twisted Product Manifolds with Applications

Sibel Gerdan Aydın

doi:10.26650/ijmath.2025.00029

Concircularly and Conharmonically Flat Warped-Twisted Product Manifolds with Applications

Abstract

In this paper, we investigate warped-twisted product manifolds that are both concircularly flat and conharmonically flat. We examine the structure of their factor manifolds under these curvature conditions. Then we characterize the factor manifolds of a warped-twisted product manifold in terms of Ricci soliton and Yamabe soliton structures. Moreover, we introduce the notions of a warped-twisted generalized Robertson-Walker spacetime and a warped-twisted standard static spacetime. We also provide some applications for concircularly flat warped-twisted product manifolds that admit these spacetime metric structures. Finally, we prove that one of the factor manifolds of these spacetimes is gradient almost 𝜁-Yamabe soliton.

Keywords

References

Agaoka, Y., Kim, B. H., Lee, H. J., 1999, Conharmonic Transformation of Twisted Product Manifolds, Mem. Fac.Integrated Arts and Sci., Hiroshima Univ., ser. IV, 25, 11-20. google scholar
Agaoka, Y., Kim, B. H., Lee, S. D., 2000, Conharmonic flat fibred Riemannian space, Mem. Fac. Integrated Arts and Sci., Hiroshima Univ., ser. IV, 26, 109-115. google scholar
Ahsan, Z., Siddiqui, S. A., 2009, Concircular Curvature Tensor and Fluid space-times, Int. J. Theor. Phys., 48, 3202-3212. google scholar
Allison, D. E., Ünal, B., 2003, Geodesic structure of standard static space-times, J. Geom. Phys., 46, 193-200. google scholar
Beem, J. K., Ehrlich, Easley, K. L., 1996, Global Lorentzian Geometry, Marcel Dekker, Second Edition; New York. google scholar
Besse, A. L., 1987, Einstein manifolds, Classics in Mathematics; Springer. google scholar
Bishop, R. L., O’Neill, B., 1969, Manifolds of negative curvature, Trans. Amer. Mat. Soc., 145(1), 1-49. google scholar
Blaga, A.M., Taştan, H.M., 2022, Gradient solitons on doubly warped product manifolds, Rep. Math. Phys., 89 (3), 319-333. google scholar

Cao, H.-D., Sun, X., Zhang, Y., 2012, On the structure of gradient Yamabe solitons, Math. Res. Lett., 19, 767-774. google scholar
Chen, B.-Y., 2017, Differential geometry of warped product manifolds and submanifolds; World Scientific. google scholar
Chen, B.-Y., Deshmukh, S., 2018, A note on Yamabe solitons, Balkan J. Geom. Appl., 23(1), 37-43. google scholar
Chen, B.-Y., 2014, A simple characterization of generalized Robertson-Walker spacetimes, Gen. Relativ. Gravit., 46, 18-33. google scholar
Chen, B.-Y., 2015, Some results on concircular vector fields and their applications to Ricci solitons, Bull. Korean Math. Soc., 52(5), 1535-1547. google scholar
Cho, J. T., Kimura, M., 2009, Ricci solitons and real hypersurfaces in a complex space form, Tohoku Math. J., 61(2), 205-212. google scholar
Chow, B., 1992, The Yamabe flow on locally conformally flat manifolds with positive Ricci curvature, Comm. Pure Appl. Math., 45, 1003-1014. google scholar
De, U. C., Shenawy, S., Ünal, B., 2020, Concircular curvature on warped product manifolds and applications, Bull. Malays. Math. Sci. Soc. 43, 3395-3409. google scholar
Dobarro, F., Ünal, B., 2004, Special standard static spacetimes, Nonlinear Anal. Theory Methods Appl., 59(5), 759-770. google scholar
Dobarro, F., Ünal, B., 2008, Curvature in special base conformal warped products, Acta. Appl. Math., 104, 1-46. google scholar
Gerdan Aydın, S., Taştan, H. M., 2022, On a certain type of warped-twisted product submanifolds, Turk. J. Math., 46(7), 2645-2662. google scholar
Gutierrez, M., Olea, B., 2012, Semi-Riemannian manifolds with a doubly warped structure, Revista Matematica Iberoamericana, 28(1), 1-24. google scholar
Güler, S., Taştan, H. M., 2022, Gradient solitons on twisted product manifolds and applications, Int. J. Geom. Methods Mod. Phys., 19(10), 2250154. google scholar
Gomes, J. N., Wang, Q., Xia, C., 2017, On the A-almost Ricci soliton, J. Geom. Phys., 114, 216-222. google scholar
Hamilton, R. S. , The Ricci flow on surfaces, Contemp. Math., 71, 237-261. google scholar
Ishii, Y. , 1957, On conharmonic transformations, Tensor N.S., 7, 73-80. google scholar
Mantica, C.A., Molinari, L.G., 2021, Doubly torqued vectors and a classification of doubly twisted and Kundt spacetimes, Gen. Relativ. Gravit., 53(48). google scholar
Mantica, C. A., Molinari, L. G., De, U. C., 2016, A condition for a perfect fluid spacetime to be a generalized Robertson-Walker spacetime, J.Math. Phys., 57(2), 022508. google scholar
Mantica, C. A., Suh, Y. J., De, U. C., 2016, A note on generalized Robertson-Walker spacetimes, Int. J. Geom. Meth. Mod. Phys., 13, 1650079. google scholar
Mantica, C. A., Molinari, L. G., 2017, Twisted Lorentzian manifolds: a characterization with torse-forming time-like unit vectors, Gen. Relativ. Gravit., 49(51). google scholar
O’Neill, B., 1983, Semi-Riemannian geometry with applications to relativity; Academic Press, San Diego. google scholar
Ponge, R., Reckziegel, H., 1993, Twisted products in pseudo-Riemannian geometry, Geom. Dedicata, 48, 15-25. google scholar
Siddiqui, S. A., Ahsan, Z., 2010, Conharmonic curvature tensor and the Space-time of General Relativity, Differential Geometry-Dynamical Systems, 12, 213-220. google scholar
Taştan, H. M., Gerdan, S., 2018, Doubly twisted product semi-invariant submanifolds of a locally product Riemannian manifold, Mathematical Advances in Pure and Applied Sciences, 1(1), 23-26. google scholar
Taştan, H. M., Gerdan Aydın, S., 2022, Warped-twisted semi-slant submanifolds, Filomat 36(5), 1587-1602. google scholar
Yano, K., 1940, Concircular geometry I. Concircular transformations, Proc. Imp. Acad. Tokyo, 16, 195-200. google scholar
Yano, K., 1940, Conformally separable quadratic differential forms, Institute of Mathematics, Tokyo Imperial Univ., 16(3), 83-86. google scholar

Details

Primary Language

English

Subjects

Pure Mathematics (Other)

Journal Section

Research Article

Authors

Sibel Gerdan Aydın ^*
0000-0001-5278-6066
Türkiye

Publication Date

December 16, 2025

Submission Date

September 9, 2025

Acceptance Date

October 30, 2025

Published in Issue

Year 2025 Volume: 3 Number: 2

DOI

https://doi.org/10.26650/ijmath.2025.00029

IZ

https://izlik.org/JA44FL78FA

Cite

RIS / Bibtex

APA

Gerdan Aydın, S. (2025). Concircularly and Conharmonically Flat Warped-Twisted Product Manifolds with Applications. Istanbul Journal of Mathematics, 3(2), 66-77. https://doi.org/10.26650/ijmath.2025.00029

AMA

1.Gerdan Aydın S. Concircularly and Conharmonically Flat Warped-Twisted Product Manifolds with Applications. Istanbul Journal of Mathematics. 2025;3(2):66-77. doi:10.26650/ijmath.2025.00029

Chicago

Gerdan Aydın, Sibel. 2025. “Concircularly and Conharmonically Flat Warped-Twisted Product Manifolds With Applications”. Istanbul Journal of Mathematics 3 (2): 66-77. https://doi.org/10.26650/ijmath.2025.00029.

EndNote

Gerdan Aydın S (December 1, 2025) Concircularly and Conharmonically Flat Warped-Twisted Product Manifolds with Applications. Istanbul Journal of Mathematics 3 2 66–77.

IEEE

[1]S. Gerdan Aydın, “Concircularly and Conharmonically Flat Warped-Twisted Product Manifolds with Applications”, Istanbul Journal of Mathematics, vol. 3, no. 2, pp. 66–77, Dec. 2025, doi: 10.26650/ijmath.2025.00029.

ISNAD

Gerdan Aydın, Sibel. “Concircularly and Conharmonically Flat Warped-Twisted Product Manifolds With Applications”. Istanbul Journal of Mathematics 3/2 (December 1, 2025): 66-77. https://doi.org/10.26650/ijmath.2025.00029.

JAMA

1.Gerdan Aydın S. Concircularly and Conharmonically Flat Warped-Twisted Product Manifolds with Applications. Istanbul Journal of Mathematics. 2025;3:66–77.

MLA

Gerdan Aydın, Sibel. “Concircularly and Conharmonically Flat Warped-Twisted Product Manifolds With Applications”. Istanbul Journal of Mathematics, vol. 3, no. 2, Dec. 2025, pp. 66-77, doi:10.26650/ijmath.2025.00029.

Vancouver

1.Sibel Gerdan Aydın. Concircularly and Conharmonically Flat Warped-Twisted Product Manifolds with Applications. Istanbul Journal of Mathematics. 2025 Dec. 1;3(2):66-77. doi:10.26650/ijmath.2025.00029