A Schur Type Theorem for Almost Cosymplectic Manifolds with Kaehlerian Leaves

Yıl 2013, Cilt: 42 Sayı: 4, 455 - 463, 01.04.2013

Nesip Aktan Gülhan Ayar İmren Bektaş

Öz

In this study, we give a Schur type theorem for almost cosymplecticmanifolds with Keahlerian leaves.

Anahtar Kelimeler

Contact Manifold, Cosymplectic Manifold, Sectional Curvature

A Schur Type Theorem for Almost Cosymplectic Manifolds with Kaehlerian Leaves

Öz

-

Anahtar Kelimeler

-

Kaynakça

• Kim, T. W. and Pak, H. K. Canonical foliations of certain classes of almost contact metric structures, Acta Math. 4 (21), 841–846, 2005.
• Dileo, G. and Pastore, A. M. Almost Kenmotsu manifolds and local symmetry, Bull. Belg. Math. Soc. Simon Stevin 14, 343–354, 2007.
• Boeck, E. and Cho, J. T. η-parallel contact metric spaces, Differential geometry and its applications 22, 275–285, 2005.
• Blair, D. E. Riemannian geometry of contact and symplectic manifolds, Progress in Mathematics, 203. (Birkhˆ auser Boston, Inc., Boston, MA, 2002.
• Vaisman, I. Conformal changes of almost contact metric manifolds, Lecture Notes in Math. (Berlin-Heidelberg-New York, 1980), 435–443.
• Kassabov, O. T. Schur’s theorem for almost Hermitian manifolds, C. R. Acad. Bulg. Sci. 54 (3), 15–18, 2001.
• Cho, J. T. Geometry of contact strongly pseudo-convex CR-manifolds, J. Korean Math. 43 (5), 1019–1045, 2006.
• Kulkarni, R. S. On a theorem of F. Shur, Journal Diff. Geom. 4, 453–456, 1970.
• Gabriel, E. V. A Schur-type Theorem on Indefinite Quaternionic Keahler Manifolds, Int. J. Contemp. Math. 11 (2), 529–536, 2007.
• Nobuhiro, I. A theorem of Schur type for locally symmetric spaces, Sci. Rep. Niigata Univ., Ser. A 25, 1–4, 1989.
• Schur, F. Ueber den Zusammenhang der Raume constanten Riemann’schen Kriimmungsmasses mit den projectiven Raumen. Math. 27, 537–567, 1886.
• Goldberg, S. I. and Yano, K. Integrability of almost cosymplectic structures, Pacific J. Math. 31, 373–382, 1969.
• Olszak, Z. On almost cosymplectic man`ıfolds, Kodai Math. J. 4, 239–250, 1981.
• Olszak, Z. Almost cosymplectic man`ıfolds with K` ahlerian leaves, Tensor N. S. 46, 117–124, 198 Kirichenko, V. F. Almost cosymplectic manifolds satisfying the axiom of φ-Pholomorphic planes (in Russian), Dokl. Akad. Nauk SSSR 273, 280–284,1983.
• Endo, H. On Ricci curvatures of almost cosymplectic manifolds, An. Stiint. Univ. ”Al. I. Cuza” Iasi, Mat. 40, 75–83, 1994.
• Blair, D. E. The theory of quasi-Sasakian structures, J. Diff. Geometry, 1, 331–345, 1967. Dacko, P. and Olszak, Z. On conformally flat almost cosymplectic manifolds with Keahlerian leaves, Rend. Sem. Mat. Univ. Pol. Torino, 56 (1), 89–103, 1998.
• Goldberg, S. I. and Yano, K. Integrability of almost cosymplectic structure, Pacific J. Math. 31 , 373–382, 1969
• Tanno, S. The standard CR structure on the unit tangent bundle Tohoku Math. J. 44 (2), 535–543, 1992.
• Blair, D. E. Contact metric manifolds satisfying a nullity condition Israel J.of Math. 91, 1–3, 189-214, 1995.