Gallot-Meyer Theorem for foliations
نویسندگان
چکیده
We study transverse conformal Killing forms on foliations and prove a Gallot-Meyer theorem for foliations. Moreover, we show that on a foliation with C-positive normal curvature, if there is a closed basic 1-form φ such that ∆Bφ = qCφ, then the foliation is transversally isometric to the quotient of a q-sphere.
منابع مشابه
Gallot-Tanno theorem for closed incomplete pseudo-Riemannian manifolds and application
In this article we extend the Gallot-Tanno theorem to closed pseudo-Riemannian manifolds. It is done by showing that if the cone over such a manifold admits a parallel symmetric 2-tensor then it is incomplete and has non zero constant curvature. An application of this result to the existence of metrics with distinct Levi-Civita connections but having the same unparametrized geodesics is given.
متن کاملLocal Prescribed Mean Curvature foliations in cosmological spacetimes
A theorem about local in time existence of spacelike foliations with prescribed mean curvature in cosmological spacetimes will be proved. The time function of the foliation is geometrically defined and fixes the diffeomorphism invariance inherent in general foliations of spacetimes. Moreover, in contrast to the situation of the more special constant mean curvature foliations, which play an impo...
متن کاملFoliated Entropy Rigidity
In this article, we develop a general foliated version of the entropy rigidity theorem and “Real Schwarz Lemma” of Besson, Courtois and Gallot.
متن کاملSome recent applications of the barycenter method in geometry
1 The Entropy Rigidity Conjecture 3 1.1 The main conjecture . . . . . . . . . . . . . . . . . . . . . . . 3 1.2 Progress . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.3 The Besson-Courtois-Gallot map . . . . . . . . . . . . . . . . 6 1.4 The degree theorem . . . . . . . . . . . . . . . . . . . . . . . 7 1.5 A related conjecture . . . . . . . . . . . . . . . . . . . . . . . 9 1...
متن کاملRigidity of horospherical foliations
M . Ratner's theorem on the rigidity of horocycle flows is extended to the rigidity of horospherical foliations on bundles over finite-volume locally-symmetric spaces of non-positive sectional curvature, and to other foliations of the same algebraic form.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2008