Some Results for Bislant and Semi-Slant Submanifolds of Semi-Riemannian Manifolds

Year 2021, Volume: 14 Issue: 2, 422 - 433, 31.08.2021

Gülşah Aydın Şekerci Abdulkadir Ceylan Çöken

https://doi.org/10.18185/erzifbed.904630

Abstract

This study looks into the bislant submanifolds of almost product semi-Riemannian manifolds that are Riemannian, semi-Riemannian and lightlike. We also state the theorems that provide the required conditions for constructing a slant submanifold from a bislant submanifold. Morever, we define the semi-slant submanifolds of locally product semi-Riemannian manifolds and discuss the integrability conditions of distributions that are invariants or slants that constitute a semi-slant submanifold.

Keywords

Semi-Riemannian, Almost product structure, Nondegenerate metric

Yarı-Riemannian Manifoldların Bislant ve Yarı-Slant Altmanifoldları İçin Bazı Sonuçlar

Abstract

Bu çalışma hemen hemen çarpım yarı-Riemann manifoldların Riemann, yarı-Riemann ve ışıkbenzer olan bislant altmanifoldlarını incelemektedir. Ayrıca, bir bislant altmanifoldundan bir slant altmanifold oluşturmak için gerekli koşulları sağlayan teoremleri ifade ediyoruz. Dahası, lokal çarpım yarı-Riemann manifoldlarının yarı-slant altmanifoldlarını tanımlıyor ve yarı-slant bir altmanifold oluşturan değişmez veya slant dağılımların integrallenebilirlik koşullarını tartışıyoruz.

Keywords

Yarı-Riemann, Hemen hemen çarpım yapısı, Dejenere olmayan metrik

References

• Aydın, G., and Çöken, A. C., 2013. “Slant submanifolds of semi-Riemannian manifolds. International Journal of Geometric Methods in Modern Physics, 10(10), 1350058.
• Chen, B. Y., 1990. “Geometry of Slant Submanifolds”. Katholieke Universiteit, Leuven.
• Duggal, L. K., and Bejancu, A., 1996. “Lightlike Submanifolds of Semi-Riemannian Manifolds and Applications”. Kluwer Academic Publishers, The Netherlands.
• Li, H., and Liu, X., 2010. “Semi-slant submanifolds of a locally product manifold”. Georgian Mathematical Journal, 12(2), 273.
• Şahin, B., 2006. “Slant submanifolds of an almost product Riemannian manifold”. J. Korean Math. Soc., 43(4), 717.
• Şahin, B., 2008. “Slant lightlike submanifolds of indefinite Hermitian manifolds”. Balkan Journal of Geometry and Its Applications, 13(1), 107.
• Yano, K., and Kon, M., 1984. “Structures on Manifolds”. World Scientific Publishing Co. Pte. Ltd., Singapore.