LP-Kosimpletik Manifoldunun Kontak Pseudo-Slant Altmanifoldların Geodeziklik Durumları

Yıl 2018, , 418 - 429, 31.07.2018

Süleyman Dirik

https://doi.org/10.17714/gumusfenbil.397059

Öz

Bir
LP-kosimpletik manifoldunda kontak pseudo-slant altmanifoldların geodeziklik
durumları için yeni sonuçlar gösterildi. Bir alt manifoldun kontak pseudo-slant
olması için gerek ve yeter şartlar verildi. Kontak pseudo-slant çarpım
karakterize edildi ve kontak pseudo-slant altmanifoldun kontak pseudo-slant
çarpım olması için gerek ve yeter şartlar verildi. Ayrıca, konuyu açıklamak için
hemen hemen parakontak metrik manifold örneği incelendi.

Anahtar Kelimeler

LP-Kosimpletik manifold, Kontak pseudo-slant, Total geodezik altmanifold

Geodesic Situations of Contact Pseudo-Slant Submanifolds in a LP-Cosymplectic Manifold

Öz

New
results are shown for the  geodesic
situations of  contact pseudo-slant
submanifolds in a LP-cosymplectic manifold. Necessary and sufficient conditions
for a submanifold to be contact pseudo-slant are given.  The contact pseudo-slant product is
characterized and necessary and sufficient conditions for a  contact pseudo-slant submanifold to be the
pseudo-slant product is given. Also, an example of a contact pseudo-slant
submanifold is investigate in an almost paracontact metric manifold to explain
the subject.

Anahtar Kelimeler

LP-Cosymplectic manifold, Contact pseudo-slant submanifold, Totally geodesic submanifold

Kaynakça

• Atçeken, M., ve Dirik, S., 2014. On the geometry of pseudo-slant submanifolds of a Kenmotsu manifold, Gulf Joural of Mathematics, 2, 51-66 .
• Atçeken, M., ve Hui, S. K., 2013. Slant and pseudo-slant submanifolds in -manifolds, Czechoslovak Mathematical Journal, 63, 138, 177-190 .
• Atçeken, M., Yıldırım, Ü. ve Dirik, S., 2017. Sub-Manifolds of a Riemannian Manifold, Manifolds: Current Research Areas, Prof. Paul Bracken , InTech, DOI:10.5772/65948.,2017.
• Cabrerizo, J. L., Carriazo, A., Fernandez, L. ve Fernandez, M., 2000. Slant submanifolds in Sasakian manifolds, Glasgow Mathhematical Journal, 42, 125-138.
• Cabrerizo, J. L., Carriazo, A., Fernandez, L. ve Fernandez, M., 2000. Structure on a Slant Submanifolds of a contact manifold, Indian Journal Pure and Applied Mathematics, 31, 7, 857-864.
• Cabrerizo, J. L., Carriazo, A., Fernandez, L. ve Fernandez, M., 1999. Slant submanifolds in Sasakian manifolds, Geomeatriae Dedicata., 78, 183-199.
• Chen, B. Y., 1990. Geometry of slant submanifolds: Katholieke Universiteit Leuven, Leuven, Belgium. View at Zentralblatt Mathematics.
• Chen, B. Y., 1990. Slant immersions, Bulletin Australian Mathematical Society, 41, 135-147.
• Chen, B. Y., 1973. Geometry of submanifolds, Pure ve Applied Mathematics, No.22., Marcel Dekker, Inc. , New York.
• Chen, B. Y., 1990. Geometry of slant submanifolds, Katholieke Universiteit Leuven.
• Dirik, S. ve Atçeken, M., 2013. Pseudo-slant submanifolds of a nearly Cosymplectic manifold, Turkish Journal of Mathematics & Computer Science, ID 20140035, pp:14.
• Dirik, S., 2014. Pseudo-Slant Altmanifoldların Geometrisi Üzerine, Doktora Tezi, Gaziosmanpaşa Üniversitesi Fen Bilimleri Enstitüsü, Tokat, 1-122 .
• Dirik, S. ve Atçeken, M., 2016. Pseudo-slant submanifold in Cosymplectic space forms, Acta Universitatis Sapientiae Mathematica, 8, 1, 53-74.
• Dirik, S. ve Atçeken, M., 2016. On the geometry of pseudo-slant submanifolds of a Cosymplectic manifold, International Electronic Journal of Geometry, 9, 1, 45-56.
• Dirik, S., Atçeken, M. ve Yıldırım, Ü., 2018. On the geometry of contact pseudo-slant submanifolds in - manifold, International Journal of Applied Mathematics and Statistics, 57, 2, 96-109.
• Dirik, S., Atçeken, M. ve Yıldırım, Ü., 2017. Contact pseudo-slant submanifolds of a normal paracontact metric manifold, International Journal of Applied Mathematics and Statistics, 56, 3, 33-41.
• De, U.C. ve Sarkar, A., 2011. On pseudo-slant submanifolds of Trans Sasakian manifold, Proceedings of the Estonian Academy of Sciences, 60, 1, 1-11.
• Khan, V. A. ve Khan, M. A., 2007. Pseudo-slant submanifolds of a Sasakian manifold, Indian Journal Prue Applied Mathematics, 38, 1, 31-42 .
• Lotta, A., 1996. Slant submanifolds in contact geometry, Bulletin Mathematical Society Roumanie, 39, 183-198.
• Lotta, A., 1998. Three-dimensional slant submanifolds of k-contact manifolds, Balkan of Journal Geometry and its Applications, 3, 1, 37-51.
• Matsumuto, K., 1989. On Loretzian paracontact manifolds, Bull. of Yamagata Univ. Nat. Sci., 12, 151-156.
• Matsumuto, K., Mihai, I. ve Rosca, R., 1995. -Null geodesic gradient vector fields ona Lorentzian para-Sasakian manifold, Journal of the Korean Mathematical Society, 32, 1, 17-31.
• Pandey, P. K. ve Gupta, R. S., 2008. Characterization of a slant submanifold of a Kenmotsu manifold, Novi Sad Journal Mathematics, 38 , 1, 97-102.
• Sarkar, A. ve Sen, M., 2012. On invariant submanifolds of LP-Sasakian manifolds, Extracta mathematcae, 21, 1, 145-154.
• Siddesha, M.S., Begawadi, C.S, Nirmala, D. ve Srikantha, N., 2017. On the geometry of pseudo-slant submanifolds of LP-cosymplectic manifold, International Journal of Mathematics And its Applications, 5 ,4, 81-87.