Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Notes on square-integrable cohomology spaces on certain foliated manifolds


Author: Shinsuke Yorozu
Journal: Trans. Amer. Math. Soc. 255 (1979), 329-341
MSC: Primary 57R30
DOI: https://doi.org/10.1090/S0002-9947-1979-0542884-6
MathSciNet review: 542884
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We discuss some square-integrable cohomology spaces on a foliated manifold with one-dimensional foliation whose leaves are compact and with a complete bundle-like metric. Applications to a contact manifold are given.


References [Enhancements On Off] (What's this?)

  • [1] A. Andreotti and E. Vesentini, Carleman estimates for the Laplace-Beltrami equation on complex manifold, Inst. Hautes Études Sci. Publ. Math. 25 (1965), 313-362. MR 30 #5333. MR 0175148 (30:5333)
  • [2] S. I. Goldberg, Curvature and homology, Academic Press, New York, 1962. MR 25 #2537. MR 0139098 (25:2537)
  • [3] L. Hörmander, $ {L^2}$-estimates and existence theorems for the $ \overline \partial $-operator, Acta Math. 113 (1965), 89-152. MR 31 #3691. MR 0179443 (31:3691)
  • [4] H. Kitahara, Remarks on square-integrable basic cohomology spaces on a foliated Riemannian manifold, Kodai Math. J. 2 (1979). MR 548394 (81f:57024)
  • [5] H. Kitahara and S. Yorozu, On the cohomology groups of a manifold with a nonintegrable subbundle, Proc. Amer. Math. Soc. 59 (1976), 201-204. MR 55 #11271. MR 0438356 (55:11271)
  • [6] Y. Ogawa, On C-harmonic forms in a compact Sasakian space, Tôhoku Math. J. 19 (1967), 267-296. MR 36 #4484. MR 0221432 (36:4484)
  • [7] K. Okamoto and H. Ozeki, On square-integrable $ \overline \partial $-cohomology spaces attached to hermitian symmetric spaces, Osaka J. Math. 4 (1967), 95-110. MR 37 #4834. MR 0229260 (37:4834)
  • [8] B. L. Reinhart, Foliated manifolds with bundle-like metrics, Ann. of Math. (2) 69 (1959), 119-131. MR 21 #6004. MR 0107279 (21:6004)
  • [9] -, Harmonic integrals on foliated manifolds, Amer. J. Math. 81 (1959), 529-536. MR 21 #6005. MR 0107280 (21:6005)
  • [10] S. Sasaki, Almost contact manifolds, Part I, Math. Inst. Tôhoku Univ. 1965; ibid., Part II, 1967; ibid., Part III, 1968. MR 0215232 (35:6075)
  • [11] S. Tachibana, On a decomposition of C-harmonic forms in a compact Sasakian space, Tôhoku Math. J. 19 (1967), 198-212. MR 36 #3379. MR 0220314 (36:3379)
  • [12] I. Vaisman, Variétés riemanniennes feuilletées, Czechoslovak Math. J. 21 (1971), 46-75. MR 44 #4776. MR 0287572 (44:4776)
  • [13] -, Cohomology and differential forms, Marcel Dekker, New York, 1973. MR 49 #6095. MR 0341344 (49:6095)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 57R30

Retrieve articles in all journals with MSC: 57R30


Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1979-0542884-6
Keywords: Riemannian foliated manifold, bundle-like metric, square-integrable cohomology
Article copyright: © Copyright 1979 American Mathematical Society

American Mathematical Society