Kodai Mathematical Journal

Almost contact structures and curvature tensors

Dirk Janssens and Lieven Vanhecke

Full-text: Open access

Article information

Source
Kodai Math. J. Volume 4, Number 1 (1981), 1-27.

Dates
First available in Project Euclid: 23 January 2006

Permanent link to this document
http://projecteuclid.org/euclid.kmj/1138036310

Digital Object Identifier
doi:10.2996/kmj/1138036310

Mathematical Reviews number (MathSciNet)
MR0615665

Zentralblatt MATH identifier
0472.53043

Subjects
Primary: 53C15: General geometric structures on manifolds (almost complex, almost product structures, etc.)
Secondary: 53C25: Special Riemannian manifolds (Einstein, Sasakian, etc.)

Citation

Janssens, Dirk; Vanhecke, Lieven. Almost contact structures and curvature tensors. Kodai Math. J. 4 (1981), no. 1, 1--27. doi:10.2996/kmj/1138036310. http://projecteuclid.org/euclid.kmj/1138036310.


Export citation

References

  • [1] M. BERGER, Le spectre des varietes emanniennes, Rev. Roumaine Math. Pures Appl., 23 (1968), 915-931.
  • [2] M. BERGER, P. GAUDUCHON & E. MAZET, Le spectre d'une variete riemannienne, Lecture Notes in Mathematics, vol. 194, Springer Verlag, Berlin and New York, 1971.
  • [3] D. BLAIR, The theory of quasi-Sasakian structures, /. Differential Geometry, 1 (1967), 331-345.
  • [4] D. BLAIR, Contact manifolds in Riemannan geometry, Lecture Notes in Mathematics, vol. 509, Springer Verlag, Berlin and New York, 1976.
  • [5] R. L. BISHOP & B. O'NEILL, Manifolds of negative curvature, Trans. Amer. Math. Soc, 145 (1969), 1-49.
  • [6] J. BOUZON, Structures presque-cocomplexes, Rend. Sem. Mat. Univ. e Politec. Torino, 24 (1964-65), 53-123.
  • [7] H. DONELLY, Topology and Einstem Kahler metrics, /. Differential Geometry, 11 (1976), 259-264.
  • [8] A. GRAY, Some relations between curvature and characteristic classes, Math. Ann., 184 (1970), 257-267.
  • [9] A. GRAY, Einstein-like manifolds which are not Einstein, Geometnae Dedicata, 7 (1978), 259-280.
  • [10] A. GRAY & L. HERVELLA, The sixteen classes of almost Hermitian manifolds and their linear invariants, Ann. Mat. Pura Appl., 123 (1980), 35-58.
  • [11] D. JANSSENS, Krommingstensoren, Decomposittetheorie en toepassingen, Doctoraatsverhandeling, Kath. Univ. Leuven, 1977.
  • [12] K. KENMOTSU, A class of almost contact Riemannian manifolds, Thoku Math. J., 24 (1972), 93-103.
  • [13] R. S. KULKARNI, On the Bianchi identities, Math. Ann., 199 (1972), 175-204.
  • [14] G. D. LUDDEN, Submanifolds of cosymplectic manifolds, Differential Geometry, 4 (1970), 237-244.
  • [15] M. MATSUMOTO & G. CHUMAN, On the C-Bochner curvature tensor, TRU Math., 5 (1969), 21-30.
  • [16] H. MORI, On the decomposition of generalized /-curvature tensor fields, Thoku Math. J., 25 (1973), 225-235.
  • [17] K. NOMIZU, On the decomposition of generalized curvature tensor fields, Differential Geometry, Kinokuniya, Tokyo, 1972, 335-345.
  • [18] M. OKUMURA, Some remarks on space with a certain contact structure, Tohoku Math. J., 14 (1962), 135-145.
  • [19] S. SASAKI, Almost contact manifolds I, II, III, Lecture Notes, Math. Institute Thoku Univ., 1965, 1967, 1968.
  • [20] I. M. SINGER & J. A. THORPE, The curvature of 4-dimensional Einstein spaces, Global Analysts (papers in honor of K. Kodaira), Univ. of Tokyo Press, Tokyo, 1969, 355-365.
  • [21] M. SITARAMAYYA, Curvature tensors in Kahler manifolds, Trans. mer. Math. Soc, 183 (1973), 341-353.
  • [22] S. TANNO, The automorphism groups of almost contact Riemannian manifolds, Tohoku Math. J., 21 (1969), 21-38.
  • [23] S. TANNO, 4-dimensional conformally flat Kahler manifolds, Tohoku Math. J., 24 (1972), 501-504.
  • [23] S. TANNO, Locally symmetric if-contact Riemannian manifolds, Proc. Japan Acad., 49 (1967), 581-583.
  • [24] L. VANHECKE, The Bochner curvature tensor on almost Hermitian manifolds, Rend. Sem. Mat. Univ. e Politec. Torino, 34 (1975-76), 21-38.
  • [25] L. VANHECKE, Almost Hermitian manifolds with /-invariant Riemannian curvature tensor, Rend. Sem. Mat. Univ. e Politec. Torino, 34 (1975-76), 487-498.
  • [26] L. VANHECKE, Antiholomorphic submanifolds of generalized complex space forms, Bull. Inst. Math. Acad. Sinica, 4 (1976), 127-140.
  • [27] L. VANHECKE, On the decomposition of curvature tensor fields on almost Hermitian manifolds, Conf. on Diff. Geometry, Proc, Michigan State Univ., 1976, 16-33.
  • [28] L. VANHECKE, The Bochner curvature tensor on almost Hermitian manifolds, Geometnae Dedicata, 6 (1977), 389-397.
  • [29] L. VANHECKE & F. BOUTEN, Constant type for almost Hermitian manifolds, Bull. Math. Soc. Math. R. S. Roumame, 20 (1976), 415-422.
  • [30] Y. WATANABE, On the characteristic functions of harmonic quaternion Kahlerian spaces, Kdai Math. Sem. Rep., 27 (1976), 410-420.
  • [31] H. WEYL, The classical groups. Their invariants and representations, Princeton Univ. Press, Princeton, 1946.
  • [32] K. YANO & M. KON, Anti-invariant submanifolds, Marcel Dekker, New York, 1976.
  • [33] Y. YOSHIMATSU, On the decomposition of generalized S-curvature-like tensor fields, Tohoku Math. J., 29 (1977), 235-254.
  • [34] F. TRICERRI & L. VANHECKE, Curvature tensors on almost Hermitian manifolds, to appear in Trans. Amer. Math. Soc.
  • [35] Y. SHIBUYA, The Spectrum of Sasakian manifolds, Kodai Math. J., 3 (1980), 197-211.