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SOME RESULTS ON PSEUDO RICCI SYMMETRIC ALMOST alpha-COSYMPLECTIC f-MANIFOLDS

Year 2013, Volume: 1 Issue: 2 , 57 - 66 , 01.12.2013
https://izlik.org/JA66BH34EU

Abstract

In this study, we consider pseudo Ricci symmetric almost α-cosymplecticf -manifolds. We get some results on pseudo Ricci symmetric α-cosymplecticf -manifolds and almost α-cosymplectic f -manifolds verifying (κ, µ, ν)-nullityconditions

References

  • Yano, K., On a structure defined by a tensor field of type (1, 1) satisfying f3+ f = 0, Tensor N. S., 14, 99-109, (1963).
  • Golberg, S, and Yano, K., Globally framed f -manifolds, Illinois J. Math. 15, 456-474, (1971). [3] Falcitelli, M. and Pastore, A. M., f -structure of Kenmotsu Type, Mediterr. J. Math. 3 549- 564, (2006).
  • Ozt¨urk H., Aktan N., Murathan C., Vanlı Turgut A., Almost α-cosymplectic f -manifolds, Annals of the Alexandru Ioan Cuza University-Mathematics, in press.
  • Blair D., Kouforgiorgos T. and Papantoniou B. J., Contact metric manifolds satisfying a nullity condition, Israel J. Math., 91 (1995), 189-214.
  • Blair D. E., Riemannian geometry of contact and symplectic manifolds, Progress in Mathe- matics, 203. Birkhˆauser Boston, Inc., Boston, MA, 2002.
  • Olszak Z., Locally conformal almost cosymplectic manifolds, Coll. Math., 57 (1989), 73–87. [8] Blair D. E. and Goldberg S. I., Topology of almost contact manifolds, J. Differential geometry, 1(1967), 347-354.
  • Goldberg S.I. and Yano K. Integrability of almost cosymplectic structures, Pasific J. Math., 31 (1969), 373-382.
  • Blair D. E., The theory of quasi-Sasakian structures, J. Diff. Geometry, 1 (1967), 331-345.
  • Cordero L. A., Fernandez M. and De Leon M., Examples of compact almost contact manifolds admitting neither Sasakian nor cosymplectic structures, Atti Sem. Mat. Univ. Modena, 34 (1985-86), 43-54.
  • Chinea D. and Gonzalez C., An example of almost cosymplectic homogeneous manifold, in: Lect. Notes Math. Vol. 1209, Springer-Verlag, Berlin-Heildelberg-New York, (1986), 133-142. [13] Olszak Z., On almost cosymplectic manifolds, Kodai Math. J., 4 (1981), 239-250.
  • Olszak Z., Almost cosymplectic manifolds with K¨ahlerian leaves, Tensor N. S., 46 (1987), 117-124. [15] Blair D. E., Goldberg S. I., Topology of almost contact manifolds, J. Diff. Geometry, 1 (1967), 347-354. [16] Chinea D., De Leon M., Marrero J. C., Topology of cosymplectic manifolds, J. Math. Pures Appl., 72 (1993), 567-591.
  • Chinea D., De Leon M., Marrero J. C., Coeffective cohomology on almost cosymplectic manifolds, Bull. Sci. Math., 119 (1995), 3-20.
  • Libermann M. P., Sur les automorphismes infinitesimaux des structures symplectiques et des structures de contact, in: Colloque de Geometrie Differentielle Globale (Bruxelles, 1958), Centre Belge de Recherche Mathematiques Louvain, (1959), 37-59.
  • Lichnerowicz A., Theoremes de reductivite sur des algebres d’automorphismes, Rend. Mat., 22 (1963), 197-244.
  • Fujimoto A. and Muto H., On cosymplectic manifolds, Tensor N. S., 28 (1974), 43-52.
  • Kirichenko V. F., Almost cosymplectic manifolds satisfying the axiom of Φ-holomorphic planes (in Russian), Dokl. Akad. Nauk SSSR, 273 (1983), 280-284.
  • Endo H., On Ricci curvatures of almost cosymplectic manifolds, An. S¸tiint. Univ. ”Al. I. Cuza” Ia¸si, Mat., 40 (1994), 75-83.
  • Boeckx E., A full classification of contact metric (κ, µ)-spaces, Illinois J. Math., 44 (1) (2000), 212-219. [24] Koufogiorgos Th.and Tsichlias C., On the existence of a new class of contact metric manifolds, Canad. Math. Bull., 43 (2000), 440-447.
  • Yano, K. and Kon, M., Structures on Manifolds, Series in Pure Math, Vol 3, World Sci, 1984. [26] Blair, D.E., Geometry of manifolds with structural group U (n) × O(s), J. Diff . Geom., 4(1970), 155-167.
  • Goldberg, S.I. and Yano, K., On normal globally framed f -manifolds, Tohoku Math. J., 22(1970), 362-370.
  • Chaki M. C., On pseudo symmetric manifolds, An. Stiint. Univ. Al. I. Cuza Iasi Sect. I a Mat., 33 (1) (1987), 53-58.
  • Chaki M. C.,On pseudo Ricci symmetric manifolds, Bulgar. J. Phys., 15 (6) (1988), 526-531. [30] Tamassy L.
  • manifolds,International
  • (Bucharest,1992). Tensor (N.S.), 53 (1993), Commemoration Volume I, 140-148. on Differential and Conference Geometry its
  • Applications [31] Tamassy L. and Binh T. Q., On weakly symmetric and weakly projective symmetric Rie- mannian manifolds, Differential geometry and its applications (Eger, 1989), 663-670, Colloq. Math. Soc. Janos Bolyai, 56, North-Holland, Amsterdam, 1992.
  • De U. C., Shaikh A. A. and Biswas S., On weakly symmetric contact metric manifolds, Tensor (N.S.), 64 (2) (2003), 170-175.
  • ¨Ozg¨ur C., On weak symmetries of Lorentzian para-Sasakian manifolds, Rad. Mat., 11 (2) (2002/03), 263-270.
  • Ozg¨ur C., On weakly symmetric Kenmotsu manifolds, Differ. Geom. Dyn. Syst., 8 (2006), 204-209. [35] Singh H. and Khan Q., On special weakly symmetric Riemannian manifolds, Publ. Math. Debrecen, Hungary 58 (2001), 523-536.
  • Aktan N., G¨org¨ul¨u A. and ¨Oz¨usa˘glam E., On Special Weakly Symmetric Kenmotsu Mani- folds, Sarajevo Journal of Mathematics, Vol.3 (15) (2007), 93-97.
  • (Yavuz Selim Balkan) Duzce University, Faculty of Art and Sciences, Department of Mathematics, Duzce/TURKEY
  • E-mail address: y.selimbalkan@gmail.com
  • (Nesip Aktan) Duzce University, Faculty of Art and Sciences, Department of Math- ematics, Duzce/TURKEY
  • E-mail address: nesipaktan@gmail.com

Year 2013, Volume: 1 Issue: 2 , 57 - 66 , 01.12.2013
https://izlik.org/JA66BH34EU

Abstract

References

  • Yano, K., On a structure defined by a tensor field of type (1, 1) satisfying f3+ f = 0, Tensor N. S., 14, 99-109, (1963).
  • Golberg, S, and Yano, K., Globally framed f -manifolds, Illinois J. Math. 15, 456-474, (1971). [3] Falcitelli, M. and Pastore, A. M., f -structure of Kenmotsu Type, Mediterr. J. Math. 3 549- 564, (2006).
  • Ozt¨urk H., Aktan N., Murathan C., Vanlı Turgut A., Almost α-cosymplectic f -manifolds, Annals of the Alexandru Ioan Cuza University-Mathematics, in press.
  • Blair D., Kouforgiorgos T. and Papantoniou B. J., Contact metric manifolds satisfying a nullity condition, Israel J. Math., 91 (1995), 189-214.
  • Blair D. E., Riemannian geometry of contact and symplectic manifolds, Progress in Mathe- matics, 203. Birkhˆauser Boston, Inc., Boston, MA, 2002.
  • Olszak Z., Locally conformal almost cosymplectic manifolds, Coll. Math., 57 (1989), 73–87. [8] Blair D. E. and Goldberg S. I., Topology of almost contact manifolds, J. Differential geometry, 1(1967), 347-354.
  • Goldberg S.I. and Yano K. Integrability of almost cosymplectic structures, Pasific J. Math., 31 (1969), 373-382.
  • Blair D. E., The theory of quasi-Sasakian structures, J. Diff. Geometry, 1 (1967), 331-345.
  • Cordero L. A., Fernandez M. and De Leon M., Examples of compact almost contact manifolds admitting neither Sasakian nor cosymplectic structures, Atti Sem. Mat. Univ. Modena, 34 (1985-86), 43-54.
  • Chinea D. and Gonzalez C., An example of almost cosymplectic homogeneous manifold, in: Lect. Notes Math. Vol. 1209, Springer-Verlag, Berlin-Heildelberg-New York, (1986), 133-142. [13] Olszak Z., On almost cosymplectic manifolds, Kodai Math. J., 4 (1981), 239-250.
  • Olszak Z., Almost cosymplectic manifolds with K¨ahlerian leaves, Tensor N. S., 46 (1987), 117-124. [15] Blair D. E., Goldberg S. I., Topology of almost contact manifolds, J. Diff. Geometry, 1 (1967), 347-354. [16] Chinea D., De Leon M., Marrero J. C., Topology of cosymplectic manifolds, J. Math. Pures Appl., 72 (1993), 567-591.
  • Chinea D., De Leon M., Marrero J. C., Coeffective cohomology on almost cosymplectic manifolds, Bull. Sci. Math., 119 (1995), 3-20.
  • Libermann M. P., Sur les automorphismes infinitesimaux des structures symplectiques et des structures de contact, in: Colloque de Geometrie Differentielle Globale (Bruxelles, 1958), Centre Belge de Recherche Mathematiques Louvain, (1959), 37-59.
  • Lichnerowicz A., Theoremes de reductivite sur des algebres d’automorphismes, Rend. Mat., 22 (1963), 197-244.
  • Fujimoto A. and Muto H., On cosymplectic manifolds, Tensor N. S., 28 (1974), 43-52.
  • Kirichenko V. F., Almost cosymplectic manifolds satisfying the axiom of Φ-holomorphic planes (in Russian), Dokl. Akad. Nauk SSSR, 273 (1983), 280-284.
  • Endo H., On Ricci curvatures of almost cosymplectic manifolds, An. S¸tiint. Univ. ”Al. I. Cuza” Ia¸si, Mat., 40 (1994), 75-83.
  • Boeckx E., A full classification of contact metric (κ, µ)-spaces, Illinois J. Math., 44 (1) (2000), 212-219. [24] Koufogiorgos Th.and Tsichlias C., On the existence of a new class of contact metric manifolds, Canad. Math. Bull., 43 (2000), 440-447.
  • Yano, K. and Kon, M., Structures on Manifolds, Series in Pure Math, Vol 3, World Sci, 1984. [26] Blair, D.E., Geometry of manifolds with structural group U (n) × O(s), J. Diff . Geom., 4(1970), 155-167.
  • Goldberg, S.I. and Yano, K., On normal globally framed f -manifolds, Tohoku Math. J., 22(1970), 362-370.
  • Chaki M. C., On pseudo symmetric manifolds, An. Stiint. Univ. Al. I. Cuza Iasi Sect. I a Mat., 33 (1) (1987), 53-58.
  • Chaki M. C.,On pseudo Ricci symmetric manifolds, Bulgar. J. Phys., 15 (6) (1988), 526-531. [30] Tamassy L.
  • manifolds,International
  • (Bucharest,1992). Tensor (N.S.), 53 (1993), Commemoration Volume I, 140-148. on Differential and Conference Geometry its
  • Applications [31] Tamassy L. and Binh T. Q., On weakly symmetric and weakly projective symmetric Rie- mannian manifolds, Differential geometry and its applications (Eger, 1989), 663-670, Colloq. Math. Soc. Janos Bolyai, 56, North-Holland, Amsterdam, 1992.
  • De U. C., Shaikh A. A. and Biswas S., On weakly symmetric contact metric manifolds, Tensor (N.S.), 64 (2) (2003), 170-175.
  • ¨Ozg¨ur C., On weak symmetries of Lorentzian para-Sasakian manifolds, Rad. Mat., 11 (2) (2002/03), 263-270.
  • Ozg¨ur C., On weakly symmetric Kenmotsu manifolds, Differ. Geom. Dyn. Syst., 8 (2006), 204-209. [35] Singh H. and Khan Q., On special weakly symmetric Riemannian manifolds, Publ. Math. Debrecen, Hungary 58 (2001), 523-536.
  • Aktan N., G¨org¨ul¨u A. and ¨Oz¨usa˘glam E., On Special Weakly Symmetric Kenmotsu Mani- folds, Sarajevo Journal of Mathematics, Vol.3 (15) (2007), 93-97.
  • (Yavuz Selim Balkan) Duzce University, Faculty of Art and Sciences, Department of Mathematics, Duzce/TURKEY
  • E-mail address: y.selimbalkan@gmail.com
  • (Nesip Aktan) Duzce University, Faculty of Art and Sciences, Department of Math- ematics, Duzce/TURKEY
  • E-mail address: nesipaktan@gmail.com
There are 33 citations in total.

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Authors

Y. Selim Balkan This is me

Nesipaktan This is me

Submission Date April 4, 2015
Publication Date December 1, 2013
IZ https://izlik.org/JA66BH34EU
Published in Issue Year 2013 Volume: 1 Issue: 2

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Vancouver 1.Y. Selim Balkan, Nesipaktan . SOME RESULTS ON PSEUDO RICCI SYMMETRIC ALMOST alpha-COSYMPLECTIC f-MANIFOLDS. Konuralp J. Math. [Internet]. 2013 Oct. 1;1(2):57-66. Available from: https://izlik.org/JA66BH34EU
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