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On the mean curvature cohomology class on foliated manifolds

박홍경|Tae Wan Kim
장전수학회 (Jangjeon Mathematical Society)|2008.01|Advanced Studies in Contemporary Mathematics|제16권 제1호|pp. 115-120

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참고문헌

키워드

mean curvaturebasic cohomologytransversally oriented foliation.
주제분류수학

초록

In this paper, we discuss with a question when a basic mean curvature formassociated to a transversally oriented foliationF on an oriented Riemannian manifold(M;g) is to be closed. Our results extend those obtained in [E-P], [Es].

Abstract

In this paper, we discuss with a question when a basic mean curvature formassociated to a transversally oriented foliationF on an oriented Riemannian manifold(M;g) is to be closed. Our results extend those obtained in [E-P], [Es].

참고문헌 (14)

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  3. D. Dominguez, "Finiteness and tenseness for Riemannian foliations", Amer. J. Math, 120, pp.1237~1276 (1998)
  4. A. El Kacimi-Alaoui, "La cohomologie basique d'un feuilletage riemannien est de dimension nie", Math. Z, 188, pp.593~599 (1985)
  5. R.H. Escobales, "The mean curvature cohomology class for foliations and the in nitesimal geometry of the leaves", Di . Geom. Appl, 2, pp.167~178 (1992)
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  7. F.W. Kamber, "Foliations and metrics", Proc. of a Year in Di . Geom., pp.103~152 (1983)
  8. H. Lawson, "Foliations", Bull. Math. Amer. Soc, 80, pp.369~418 (1974)
  9. X.M. Masa, "Duality and minimality in Riemannian foliations", Comment. Math. Helv, 67, pp.17~27 (1992)
  10. B. O'Neill, "The fundamental equations of a submersion", Michigan Math. J, 13, pp.459~469 (1966)
  11. B. Reinhart, "Harmonic integrals on foliated manifolds", Amer. J. Math, 91, pp.529~536 (1959)
  12. H. Rummler, "Quelques notions simples en geometrie riemannienne et leurs applications aux feuilletages compacts", Comment. Math. Helv, 54, pp.224~239 (1979)
  13. D. Sullivan, "Cycles for the dynamical study of foliated manifolds and complex manifolds", Invent. Math, 36, pp.225~255 (1976)
  14. K. Yano, "Integral formulas in Riemannian geometry" (1970), Marcel Dekker, Inc.

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