Summary
In this paper, we completely characterize the local structure of trans-Sasakian manifolds of dimension ⩾ 5 by giving suitable examples.
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References
D. E. Blair,The theory of quasi-Sasakian structures, J. Diff. Geom.,1 (1967), pp. 331–345.
D. E.Blair,Contact manifolds in Riemannian geometry, Lecture Notes in Math,509, Springer (1976).
L. A. Cordero -M. Fernandez -M. De Leon,Examples of compact almost contact manifolds admitting neither Sasakian nor cosymplectic structures, Atti. Sem. Mat. Fis. Univ. Modena,34 (1985–86), pp. 43–54.
D. Chinea -C. Gonzalez,A classification of almost contact metric manifolds, Ann. Mat. Pura Appl., (IV),156 (1990), pp. 15–36.
A. Fujimoto -H. Muto,On cosymplectic manifolds, Tensor,28 (1974), pp. 43–52.
A. Gray -L. M. Hervella,The sixteen-classes of almost Hermitian manifolds and their linear invariants, Ann. Mat. Pura Appl., (IV),123 (1980), pp. 35–58.
Y. Haraguchi,Sur une généralisation des structures de contact, Thèse, Univ. du Haute Alsace, Mulhouse (1981).
D. Janssens -L. Vanhecke,Almost contact structures and curvature tensor, Kodai Math. J.,4 (1981), pp. 1–27.
K. Kenmotsu,A class of almost contact Riemannian manifolds, Tohoku Math. J.,24 (1972), pp. 93–103.
P. Libermann,Sur les structures presque complexes et autres structures infinitesimales regulieres, Bull. Soc. Mat. France,83 (1955), pp. 195–224.
J. Oubina,New classes of almost contact metric structures, Publicationes Mathematicae,32 (1985), pp. 187–193.
Z. Olszak,Normal almost contact metric manifolds of dimension three, Ann. Polon. Math.,47 (1986), no. 1, pp. 41–50.
S. Sasaki -Y. Hatakeyama,On differentiable manifolds with certain structures which are closely related to almost contact structure — II, Tôhoku Math. J.,13 (1961), pp. 281–294.
S. Sasaki -Y. Hatakeyama,On differentiable manifolds with contact metric structures, J. Math. Soc. Japan,14 (1962), pp. 249–271.
I. Vaisman,On locally conformal almost Kähler manifolds, Israel J. Math.,24 (1976), pp. 338–351.
I. Vaisman,Locally conformai Kähler manifolds with parallel Lee form, Rend. Mat. Roma,12 (1979), pp. 263–284.
I. Vaisman,Generalized Hopf manifolds, Geometriae Dedicata,13 (1982), pp. 231–255.
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Work supported by the «Consejería de Educación del Gobierno de Canarias».
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Marrero, J.C. The local structure of trans-Sasakian manifolds. Annali di Matematica pura ed applicata 162, 77–86 (1992). https://doi.org/10.1007/BF01760000
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DOI: https://doi.org/10.1007/BF01760000