Mustafa GÖK

5422

The de Rham Cohomology Group of a Hemi-Slant Submanifold in Metallic Riemannian Manifolds

In this study, we answer the question under what conditions a hemi-slant submanifold of locally decomposable metallic Riemannian manifolds admits a well defined canonical de Rham cohomology class. Firstly, we give the integrability and minimality conditions of the distributions arose from its definition. Later, we find some necessary conditions depending on the above-named concepts of the associated distributions for such a type of submanifold to define a de Rham cohomology class. Furthermore, we analyzed the non-triviality of this cohomology class In the end, we construct two examples which enable better expressing the main results.
Keywords:

De Rham cohomology group, metallic Riemannian manifold, hemi-slant submanifold Riemannian submanifold,

PDF

___

  • Bejancu, A.: Geometry of CR Submanifolds. D. Reidel Publishing Company, Dordrecht (1986).
  • Bhatt, L., Dube, K. K.: On CR-submanifold of nearly and closely para cosymplectic manifolds. Demonstratio Math. 35 (2), 405-413 (2002).
  • Blaga, A. M., Hreţcanu, C. E.: Invariant, anti-invariant and slant submanifolds of a metallic Riemannian manifold. Novi Sad J. Math. 48 (2), 55-80 (2018).
  • Blaga, A. M., Nannicini, A.: Foliations induced by metallic structures. Preprint arXiv:1903.04006 (2019).
  • Cabrerizo, J. L., Carriazo, A., Fernández, L. M., Fernández, M.: Semi-slant submanifolds of a Sasakian manifold. Geom. Dedicata 78 (2), 183-199 (1999).
  • Cabrerizo, J. L., Carriazo, A., Fernández, L. M., Fernández, M.: Slant submanifolds in Sasakian manifolds. Glasg. Math. J. 42 (1), 125-138 (2000).
  • Carriazo, A.: New Developments in Slant Submanifolds Theory. Narosa Publishing House, New Delhi (2002).
  • Chen, B. Y.: Cohomology of CR submanifolds. Ann. Fac. Sci. Toulouse Math. (5) 3 (2), 167-172 (1981).
  • Chen, B. Y.: Slant immersions. Bull. Aust. Math. Soc. 41 (1), 135-147 (1990).
  • Chen, B. Y.: Geometry of Slant Submanifolds. Katholieke Universiteit Leuven, Leuven (1990).
  • Crâşmăreanu, M. C., Hreţcanu, C. E.: Golden differential geometry. Chaos Solitons Fractals 38 (5), 1229-1238 (2008).
  • Deshmukh, S.: Cohomology of CR-submanifolds of a nearly Kaehler manifold. Math. Chronicle 16, 47-57 (1982).
  • Ghazal, T.: Cohomology of CR-submanifolds of a quasi-Kaehler manifolds. Int. J. Pure Appl. Math. 52 (5), 711-715 (2009).
  • Gök, M.: Cohomology of semi-invariant submanifolds in metallic Riemannian manifolds. Int. J. Geom. Methods Mod. Phys. https://doi.org/10.1142/S0219887822501390 (Accepted)
  • Gök, M., Kılıç, E., Özgür, C.: f_{(a,b)}(3,2,1)-structures on manifolds. J. Geom. Phys., 169, 104346 (2021).
  • Hreţcanu, C. E., Crâşmăreanu, M. C.: On some invariant submanifolds in a Riemannian manifold with golden structure. An. Ştiinţ. Univ. Al. I. Cuza Iaşi. Mat. (N.S.) 53 (suppl. 1), 199-211 (2007).
  • Hreţcanu, C. E., Blaga, A. M.: Warped product submanifolds in metallic Riemannian manifolds. Tamkang J. Math. 51 (3), 161-186 (2020).
  • Hreţcanu, C. E., Crâşmăreanu, M. C.: Applications of the golden ratio on Riemannian manifolds. Turkish J. Math. 33 (2), 179-191 (2009).
  • Hreţcanu, C. E., Crâşmăreanu, M. C.: Metallic structures on Riemannian manifolds. Rev. Un. Mat. Argentina 54 (2), 15-27 (2013).
  • Hreţcanu, C. E., Blaga, A. M.: Submanifolds in metallic Riemannian manifolds. Differ. Geom. Dyn. Syst. 20, 83-97 (2018).
  • Hreţcanu, C. E., Blaga, A. M.: Slant and semi-slant submanifolds in metallic Riemannian manifolds. J. Funct. Spaces 2018, 2864263 (2018).
  • Hreţcanu, C. E., Blaga, A. M.: Hemi-slant submanifolds in metallic Riemannian manifolds. Carpathian J. Math. 35 (2), 59-68 (2019).
  • Hreţcanu, C. E., Blaga, A. M.: Types of submanifolds in metallic Riemannian manifolds: A short survey. Mathematics 9 (19), 2467 (2021).
  • Ianuş, S., Marchiafava, S., Vîlcu, G. E.: Paraquaternionic CR-submanifolds of paraquaternionic Kähler manifolds and semi-Riemannian submersions. Cent. Eur. J. Math. 8 (4), 735-753 (2010).
  • Khan, V. A., Khan, M. A.: Pseudo-slant submanifolds of a Sasakian manifold. Indian J. Pure Appl. Math., 38 (1), 31-42 (2007).
  • Lotta, A.: Slant submanifolds in contact geometry. Bull. Math. Soc. Sci. Math. Roumanie (N.S.) 39(87) (1-4), 183-198 (1996).
  • Martin, D.: Manifold Theory. Horwood Publishing, Chichester (2002).
  • Papaghiuc, N.: Semi-slant submanifolds of a Kaehlerian manifold. An. Ştiinţ. Univ. Al. I. Cuza Iaşi. Mat. (N.S.) 40 (1), 55-61 (1994).
  • Pitis, G.: On some submanifolds of a locally product manifold. Kodai Math. J. 9 (3), 327-333 (1986).
  • Renteln, P.: Manifolds, Tensors, and Forms. Cambridge University Press, New York (2014).
  • Şahin, B.: Slant submanifolds of an almost product Riemannian manifold. J. Korean Math. Soc. 43 (4), 717-732 (2006).
  • Şahin, B.: Warped product submanifolds of Kaehler manifolds with a slant factor. Ann. Pol. Math. 95 (3), 207-226 (2009).
  • Şahin, F.: Cohomology of hemi-slant submanifolds of a Kaehler manifold. J. Adv. Stud. Topol. 5 (2), 27-31 (2014).
International Electronic Journal of Geometry-Cover
  • Yayın Aralığı: Yılda 2 Sayı
  • Başlangıç: 2008
  • Yayıncı: Prof.Dr. H.Hilmi Hacısalioğlu
Arşiv
Sayıdaki Diğer Makaleler

Alberto CAVİCCHİOLİ, Fulvia SPAGGİARİ

Haohao WANG, Jerzy WOJDYLO

Reza MİRZAİE, Omid REZAİE

Aliya Naaz SIDDIQUI, Siraj UDDİN, Mohammad Hasan SHAHİD

Duygu ÇAĞLAR, Nurten GÜRSES

Mustafa GÖK

Narmina GURBANOVA

Bilal Eftal ACET, Feyza Esra ERDOĞAN, Selcen YÜKSEL PERKTAŞ

Lorenz HALBEISEN, Norbert HUNGERBÜHLER, Juan LÄUCHLİ

Peter HORAK, Dongryul KİM