A SCHUR TYPE THEOREM FOR ALMOST 􀀀COSYMPLECTIC MANIFOLDS WITH KAEHLERIAN LEAVES

Gülhan Ayar; Mustafa Yıldırım; Nesip Aktan

Research Article

A SCHUR TYPE THEOREM FOR ALMOST 􀀀COSYMPLECTIC MANIFOLDS WITH KAEHLERIAN LEAVES

Year 2016, Volume: 4 Issue: 1, 211 - 224, 01.04.2016

Gülhan Ayar , Mustafa Yıldırım , Nesip Aktan

Abstract

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

Keywords

Contact Manifold, Cosymplectic Manifold, Sectional Curvature

References

[1] T. W. Kim, H. K. Pak, Canonical foliations of certain classes of almost contact metric structures, Acta Math. Sinica, Eng. Ser. Aug., 21, 4 (2005), 841{846.
[2] G. Dileo, A. M. Pastore, Almost Kenmotsu manifolds and local symmetry, Bull. Belg. Math. Soc. Simon Stevin, 14 (2007), 343{354.
[3] E. Boeckx, J. T. Cho, -parallel contact metric spaces, Dierential geometry and its applications, 22 (2005), 275{285.
[4] D. E., Blair, Riemannian geometry of contact and symplectic manifolds, Progress in Mathematics, 203. Birkh^auser Boston, Inc., Boston, MA, (2002).
[5] I. Vaisman, Conformal changes of almost contact metric manifolds, Lecture Notes in Math., Berlin-Heidelberg-New York, 792 (1980), 435{443.
[6] Kassabov, O. T. , Schur's theorem for almost Hermitian manifolds, C. R. Acad. Bulg. Sci. (54) 3, 15-18, 2001.
[7] Cho, J. T. ,Geometry of contact strongly pseudo-convex CR-manifolds, J. Korean Math. (43) 5, 1019-1045, 2006.
[8] Kulkarni, R. S. , On a theorem of F. Schur, Journal Di. Geom. (4), 453-456, 1970.
[9] Gabriel, E. V. , A Schur-type Theorem on Indenite Quaternionic Keahler Manifolds, Int. J. Contemp. Math. 11 (2), 529 - 536, 2007.
[10] Nobuhiro, I., A theorem of Schur type for locally symmetric spaces, Sci. Rep. Niigata Univ., Ser. A (25), 1-4,.1989.
[11] Schur, F. , Ueber den Zusammenhang der Raume constanten Riemann'schen Kriimmungs- masses mit den projectiven Raumen. Math. (27), 537-567, 1886.
[12] Goldberg, S. I. and Yano, K. , Integrability of almost cosymplectic structures, Pacic J. Math. (31), 373-382, 1969.
[13] Olszak, Z., On almost cosymplectic manfolds, Kodai Math. J. (4), 239-250, 1981.
[14] Olszak, Z., Almost cosymplectic manfolds with Kahlerian leaves, Tensor N. S. (46), 117-124, 1987.
[15] Kirichenko, V. F. , Almost cosymplectic manifolds satisfying the axiom of <Pholomorphic planes (in Russian), Dokl. Akad. Nauk SSSR ( 273), 280-28,1983.
[16] Endo, H. , On Ricci curvatures of almost cosymplectic manifolds, An. Stiinj:Univ:"Al:I:Cuza"Iaxi;Mat:(40); 75 􀀀 83; 1994:
[17] Blair, D. E. , The theory of quasi-Sasakian structures, J. Di. Geometry, (1), 331-345, 1967.
[18] Dacko, P. and Olszak, Z., On conformally at almost cosymplectic manifolds with Keahlerian leaves, Rend. Sem. Mat. Univ. Pol. Torino, (56) 1, 89-103, 1998.
[19] Goldberg, S. I. and Yano, K. , Integrability of almost cosymplectic structure, Pacic J. Math. (31) , 373{382, 1969
[20] Tanno, S. , The standard CR structure on the unit tangent bundle Tohoku Math. J. 44 (2), 535-543, 1992.
[21] Blair, D. E. , Contact metric manifolds satisfying a nullity condition Israel J.of Math. (91), 1-3, 189-214, 1995..
[22] Nesip Aktan, Gulhan Ayar and Imren Bektas, A Schur type theorem for almost cosymplectic manifolds with Kaehlerian leaves, Hacettepe Journal of Mathematics and Statistics Volume 42 (4) (2013), 455 { 463
[23] H. Ozturk, Nesip Aktan, Cengizhan Murathan, Almost -Cosymplectic ( ; ; )-Spaces, arXiv:1007.0527
[24] K. Kenmotsu, A class of contact Riemannian manifold, Tohoku Math. Journal, 24 (1972),93{ 103

Year 2016, Volume: 4 Issue: 1, 211 - 224, 01.04.2016

Gülhan Ayar , Mustafa Yıldırım , Nesip Aktan

Abstract

References

[1] T. W. Kim, H. K. Pak, Canonical foliations of certain classes of almost contact metric structures, Acta Math. Sinica, Eng. Ser. Aug., 21, 4 (2005), 841{846.
[2] G. Dileo, A. M. Pastore, Almost Kenmotsu manifolds and local symmetry, Bull. Belg. Math. Soc. Simon Stevin, 14 (2007), 343{354.
[3] E. Boeckx, J. T. Cho, -parallel contact metric spaces, Dierential geometry and its applications, 22 (2005), 275{285.
[4] D. E., Blair, Riemannian geometry of contact and symplectic manifolds, Progress in Mathematics, 203. Birkh^auser Boston, Inc., Boston, MA, (2002).
[5] I. Vaisman, Conformal changes of almost contact metric manifolds, Lecture Notes in Math., Berlin-Heidelberg-New York, 792 (1980), 435{443.
[6] Kassabov, O. T. , Schur's theorem for almost Hermitian manifolds, C. R. Acad. Bulg. Sci. (54) 3, 15-18, 2001.
[7] Cho, J. T. ,Geometry of contact strongly pseudo-convex CR-manifolds, J. Korean Math. (43) 5, 1019-1045, 2006.
[8] Kulkarni, R. S. , On a theorem of F. Schur, Journal Di. Geom. (4), 453-456, 1970.
[9] Gabriel, E. V. , A Schur-type Theorem on Indenite Quaternionic Keahler Manifolds, Int. J. Contemp. Math. 11 (2), 529 - 536, 2007.
[10] Nobuhiro, I., A theorem of Schur type for locally symmetric spaces, Sci. Rep. Niigata Univ., Ser. A (25), 1-4,.1989.
[11] Schur, F. , Ueber den Zusammenhang der Raume constanten Riemann'schen Kriimmungs- masses mit den projectiven Raumen. Math. (27), 537-567, 1886.
[12] Goldberg, S. I. and Yano, K. , Integrability of almost cosymplectic structures, Pacic J. Math. (31), 373-382, 1969.
[13] Olszak, Z., On almost cosymplectic manfolds, Kodai Math. J. (4), 239-250, 1981.
[14] Olszak, Z., Almost cosymplectic manfolds with Kahlerian leaves, Tensor N. S. (46), 117-124, 1987.
[15] Kirichenko, V. F. , Almost cosymplectic manifolds satisfying the axiom of <Pholomorphic planes (in Russian), Dokl. Akad. Nauk SSSR ( 273), 280-28,1983.
[16] Endo, H. , On Ricci curvatures of almost cosymplectic manifolds, An. Stiinj:Univ:"Al:I:Cuza"Iaxi;Mat:(40); 75 􀀀 83; 1994:
[17] Blair, D. E. , The theory of quasi-Sasakian structures, J. Di. Geometry, (1), 331-345, 1967.
[18] Dacko, P. and Olszak, Z., On conformally at almost cosymplectic manifolds with Keahlerian leaves, Rend. Sem. Mat. Univ. Pol. Torino, (56) 1, 89-103, 1998.
[19] Goldberg, S. I. and Yano, K. , Integrability of almost cosymplectic structure, Pacic J. Math. (31) , 373{382, 1969
[20] Tanno, S. , The standard CR structure on the unit tangent bundle Tohoku Math. J. 44 (2), 535-543, 1992.
[21] Blair, D. E. , Contact metric manifolds satisfying a nullity condition Israel J.of Math. (91), 1-3, 189-214, 1995..
[22] Nesip Aktan, Gulhan Ayar and Imren Bektas, A Schur type theorem for almost cosymplectic manifolds with Kaehlerian leaves, Hacettepe Journal of Mathematics and Statistics Volume 42 (4) (2013), 455 { 463
[23] H. Ozturk, Nesip Aktan, Cengizhan Murathan, Almost -Cosymplectic ( ; ; )-Spaces, arXiv:1007.0527
[24] K. Kenmotsu, A class of contact Riemannian manifold, Tohoku Math. Journal, 24 (1972),93{ 103

There are 24 citations in total.

Details

Primary Language	English
Subjects	Engineering
Journal Section	Articles
Authors	Gülhan Ayar Mustafa Yıldırım Nesip Aktan
Publication Date	April 1, 2016
Submission Date	July 10, 2014
Published in Issue	Year 2016 Volume: 4 Issue: 1

Cite

APA	Ayar, G., Yıldırım, M., & Aktan, N. (2016). A SCHUR TYPE THEOREM FOR ALMOST 􀀀COSYMPLECTIC MANIFOLDS WITH KAEHLERIAN LEAVES. Konuralp Journal of Mathematics, 4(1), 211-224.
AMA	Ayar G, Yıldırım M, Aktan N. A SCHUR TYPE THEOREM FOR ALMOST 􀀀COSYMPLECTIC MANIFOLDS WITH KAEHLERIAN LEAVES. Konuralp J. Math. April 2016;4(1):211-224.
Chicago	Ayar, Gülhan, Mustafa Yıldırım, and Nesip Aktan. “A SCHUR TYPE THEOREM FOR ALMOST 􀀀COSYMPLECTIC MANIFOLDS WITH KAEHLERIAN LEAVES”. Konuralp Journal of Mathematics 4, no. 1 (April 2016): 211-24.
EndNote	Ayar G, Yıldırım M, Aktan N (April 1, 2016) A SCHUR TYPE THEOREM FOR ALMOST 􀀀COSYMPLECTIC MANIFOLDS WITH KAEHLERIAN LEAVES. Konuralp Journal of Mathematics 4 1 211–224.
IEEE	G. Ayar, M. Yıldırım, and N. Aktan, “A SCHUR TYPE THEOREM FOR ALMOST 􀀀COSYMPLECTIC MANIFOLDS WITH KAEHLERIAN LEAVES”, Konuralp J. Math., vol. 4, no. 1, pp. 211–224, 2016.
ISNAD	Ayar, Gülhan et al. “A SCHUR TYPE THEOREM FOR ALMOST 􀀀COSYMPLECTIC MANIFOLDS WITH KAEHLERIAN LEAVES”. Konuralp Journal of Mathematics 4/1 (April 2016), 211-224.
JAMA	Ayar G, Yıldırım M, Aktan N. A SCHUR TYPE THEOREM FOR ALMOST 􀀀COSYMPLECTIC MANIFOLDS WITH KAEHLERIAN LEAVES. Konuralp J. Math. 2016;4:211–224.
MLA	Ayar, Gülhan et al. “A SCHUR TYPE THEOREM FOR ALMOST 􀀀COSYMPLECTIC MANIFOLDS WITH KAEHLERIAN LEAVES”. Konuralp Journal of Mathematics, vol. 4, no. 1, 2016, pp. 211-24.
Vancouver	Ayar G, Yıldırım M, Aktan N. A SCHUR TYPE THEOREM FOR ALMOST 􀀀COSYMPLECTIC MANIFOLDS WITH KAEHLERIAN LEAVES. Konuralp J. Math. 2016;4(1):211-24.

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