Notes on square-integrable cohomology spaces on certain foliated manifolds
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- by Shinsuke Yorozu
- Trans. Amer. Math. Soc. 255 (1979), 329-341
- DOI: https://doi.org/10.1090/S0002-9947-1979-0542884-6
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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
- Aldo Andreotti and Edoardo Vesentini, Carleman estimates for the Laplace-Beltrami equation on complex manifolds, Inst. Hautes Études Sci. Publ. Math. 25 (1965), 81–130. MR 175148, DOI 10.1007/BF02684398
- Samuel I. Goldberg, Curvature and homology, Pure and Applied Mathematics, Vol. XI, Academic Press, New York-London, 1962. MR 0139098
- Lars Hörmander, $L^{2}$ estimates and existence theorems for the $\bar \partial$ operator, Acta Math. 113 (1965), 89–152. MR 179443, DOI 10.1007/BF02391775
- Haruo Kitahara, Remarks on square-integrable basic cohomology spaces on a foliated Riemannian manifold, Kodai Math. J. 2 (1979), no. 2, 187–193. MR 548394
- Haruo Kitahara and Shinsuke Yorozu, On the cohomology groups of a manifold with a nonintegrable subbundle, Proc. Amer. Math. Soc. 59 (1976), no. 2, 201–204. MR 438356, DOI 10.1090/S0002-9939-1976-0438356-2
- Yôsuke Ogawa, On $C$-harmonic forms in a compact Sasakian space, Tohoku Math. J. (2) 19 (1967), 267–296. MR 221432, DOI 10.2748/tmj/1178243277
- Kiyosato Okamoto and Hideki Ozeki, On square-integrable $\bar \partial$-cohomology spaces attached to hermitian symmetric spaces, Osaka Math. J. 4 (1967), 95–110. MR 229260
- Bruce L. Reinhart, Foliated manifolds with bundle-like metrics, Ann. of Math. (2) 69 (1959), 119–132. MR 107279, DOI 10.2307/1970097
- Bruce L. Reinhart, Harmonic integrals on foliated manifolds, Amer. J. Math. 81 (1959), 529–536. MR 107280, DOI 10.2307/2372756
- Shigeo Sasaki, On almost contact manifolds, Proc. U.S.-Japan Seminar in Differential Geometry (Kyoto, 1965) Nippon Hyoronsha, Tokyo, 1966, pp. 128–136. MR 0215232
- Shun-ichi Tachibana, On a decomposition of $C$-harmonic forms in a compact Sasakian space, Tohoku Math. J. (2) 19 (1967), 198–212. MR 220314, DOI 10.2748/tmj/1178243317
- Izu Vaisman, Variétés riemanniennes feuilletées, Czechoslovak Math. J. 21(96) (1971), 46–75 (French). MR 287572
- Izu Vaisman, Cohomology and differential forms, Pure and Applied Mathematics, vol. 21, Marcel Dekker, Inc., New York, 1973. Translation editor: Samuel I. Goldberg. MR 0341344
Bibliographic Information
- © Copyright 1979 American Mathematical Society
- 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