Abstract
In this work we study a codimension-one C∞-foliation \({cal F}\) of a complete Riemannian manifold M. We assume that \({cal F}\) is transversely orientable. Under this hypothesis, we show that the mean curvature function of \({cal F}\) has a superior limit. Using this result, we find a necessary and sufficient condition for the foliation \({cal F}\) to be totally geodesic.
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Gomes, A.: Curvatura Média de Folheações Transversalmente Orientáveis, Tese de Doutoramento, IME-Universidade de São Paulo (2003).
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Gomes, A. The Mean Curvature of a Transversely Orientable Foliation. Results. Math. 46, 31–36 (2004). https://doi.org/10.1007/BF03322868
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DOI: https://doi.org/10.1007/BF03322868