Submanifolds of almost poly-Norden Riemannian manifolds

Our aim in the present paper is to initiate the study of submanifolds in an almost poly-Norden Riemannianmanifold, which is a new type of manifold first introduced by Şahin [17]. We give fundamental properties of submanifoldsequipped with induced structures provided by almost poly-Norden Riemannian structures and find some conditionsfor such submanifolds to be totally geodesics. We introduce some subclasses of submanifolds in almost poly-NordenRiemannian manifolds such as invariant and antiinvariant submanifolds. We investigate conditions for a hypersurface ofalmost poly-Norden Riemannian manifolds to be invariant and totally geodesic, respectively, by using the components ofthe structure induced by the almost poly-Norden Riemannian structure of the ambient manifold. We also obtain somecharacterizations for totally umbilical hypersurfaces and give some examples of invariant and noninvariant hypersurfaces.

PDF

___

[1] Acet BE. Lightlike hypersurfaces of metallic semi-Riemannian manifolds. International Journal of Geometric Methods in Modern Physics 2018; 15: 12. doi: 10.1142/S0219887818502018
[2] Adati T. Submanifolds of an almost product Riemannian manifold. Kodai Mathematical Journal 1981; 4 (2): 327- 343.
[3] Blaga AM, Hretcanu CE. Invariant, anti-invariant and slant submanifolds of a metallic Riemannian manifold. Novi Sad Journal of Mathematics 2018; 48 (2): 57-82. doi: 10.30755/NSJOM.06365
[4] Crasmareanu M, Hretcanu CE. Golden differential geometry. Chaos, Solitons & Fractals 2008; 38 (5): 1229-1238.
[5] De Spinadel VW. The metallic means family and multifractal spectra. Nonlinear Analysis Series B: Real World Applications 1999; 36 (6): 721-745.
[6] Erdoğan FE. Transversal lightlike submanifolds of metallic semi-Riemannian manifolds. Turkish Journal of Mathematics 2018; 42 (6): 3133-3148. doi: 10.3906/mat-1804-88
[7] Erdoğan FE, Yıldırım C. Semi-invariant submanifolds of golden Riemannian manifolds. In: 2nd International Conference on Advances in Natural and Applied Sciences-AIP Conference Proceedings; 2017. doi: 10.1063/1.4981692
[8] Erdoğan FE, Yıldırım C. On a study of the totally umbilical semi-invariant submanifolds of golden Riemannian manifolds. Journal of Polytechnic 2018; 21 (4): 967-970. doi: 10.2339/politeknik.389629
[9] Gezer A, Cengiz N, Salimov A. On integrability of golden Riemannian structures. Turkish Journal of Mathematics 2013; 37(4): 693-703. doi: 10.3906/mat-1108-35
[10] Hretcanu CE, Blaga AM. Submanifolds in metallic Riemannian manifolds. Differential Geometry-Dynamical Systems 2018; 20: 83-97.
[11] Hretcanu CE, Blaga AM. Slant and semi-slant submanifolds in metallic Riemannian manifolds. Journal of Function Spaces 2018; 2018: 2864263. doi: 10.1155/2018/2864263
[12] Hretcanu CE, Crasmareanu M. On some invariant submanifolds in a Riemannian manifold with golden structure. Analele Stiintifice Ale Universitatii Al. I. Cuza Din Iasi (S.N.) Matematica 2007; 53: 199-211.
[13] Hretcanu CE, Crasmareanu M. Applications of the golden ratio on Riemannian manifolds. Turkish Journal of Mathematics 2009; 33 (2): 179-191. doi: 10.3906/mat-0711-29
[14] Hretcanu CE, Crasmareanu M. Metallic structures on Riemannian manifolds. Revista de la Union Matematica Argentina 2013; 54 (2): 15-27.
[15] Kalia S. The generalizations of the golden ratio: their powers, continued fractions, and convergents. Cambridge, MA, USA: MIT. Available at http://math.mit.edu/research/highschool/primes/papers.php.
[16] Önen Poyraz N, Yaşar E. Lightlike hypersurfaces of a golden semi-Riemannian manifold. Mediterranean Journal of Mathematics 2017; 14 (5): 204. doi: 10.1007/s00009-017-0999-2
[17] Şahin B. Almost poly-Norden manifolds. International Journal of Maps in Mathematics 2018; 1 (1): 68-79

ISSN: 1300-0098
Yayın Aralığı: Yılda 6 Sayı
Yayıncı: TÜBİTAK

Arşiv