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

Gülhan Ayar; Mustafa Yıldırım; Nesip Aktan

Araştırma Makalesi

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

Yıl 2016, Cilt: 4 Sayı: 1, 211 - 224, 01.04.2016

Gülhan Ayar , Mustafa Yıldırım , Nesip Aktan

Öz

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

Anahtar Kelimeler

Contact Manifold, Cosymplectic Manifold, Sectional Curvature

Kaynakça

[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

Yıl 2016, Cilt: 4 Sayı: 1, 211 - 224, 01.04.2016

Gülhan Ayar , Mustafa Yıldırım , Nesip Aktan

Öz

Kaynakça

[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

Toplam 24 adet kaynakça vardır.

Ayrıntılar

Birincil Dil	İngilizce
Konular	Mühendislik
Bölüm	Articles
Yazarlar	Gülhan Ayar Mustafa Yıldırım Nesip Aktan
Yayımlanma Tarihi	1 Nisan 2016
Gönderilme Tarihi	10 Temmuz 2014
Yayımlandığı Sayı	Yıl 2016 Cilt: 4 Sayı: 1

Kaynak Göster

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. Nisan 2016;4(1):211-224.
Chicago	Ayar, Gülhan, Mustafa Yıldırım, ve Nesip Aktan. “A SCHUR TYPE THEOREM FOR ALMOST 􀀀COSYMPLECTIC MANIFOLDS WITH KAEHLERIAN LEAVES”. Konuralp Journal of Mathematics 4, sy. 1 (Nisan 2016): 211-24.
EndNote	Ayar G, Yıldırım M, Aktan N (01 Nisan 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, ve N. Aktan, “A SCHUR TYPE THEOREM FOR ALMOST 􀀀COSYMPLECTIC MANIFOLDS WITH KAEHLERIAN LEAVES”, Konuralp J. Math., c. 4, sy. 1, ss. 211–224, 2016.
ISNAD	Ayar, Gülhan vd. “A SCHUR TYPE THEOREM FOR ALMOST 􀀀COSYMPLECTIC MANIFOLDS WITH KAEHLERIAN LEAVES”. Konuralp Journal of Mathematics 4/1 (Nisan 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 vd. “A SCHUR TYPE THEOREM FOR ALMOST 􀀀COSYMPLECTIC MANIFOLDS WITH KAEHLERIAN LEAVES”. Konuralp Journal of Mathematics, c. 4, sy. 1, 2016, ss. 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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