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We generalize the concept of warped manifold to Riemannian submersions π: M → B between two compact Riemannian manifolds $(M, g_{M})$ and $(B, g_{B})$ in the following way. If f: B → (0,∞) is a smooth function on B which is extended to a function f̂ = f ∘ π constant along the fibres of π then we define a new metric $g_{f}$ on M by $g_{f} |_{\times} \equiv g_{M} |_{\times}, g_{f} {|_{\times T M ̂} \equiv f ̂ ² g_{M} |}_{\times T M ̂}$ , where and denote the bundles of horizontal and vertical vectors. The manifold $(M, g_{f})$ obtained that way is called a warped submersion. The function f is called a warping function. We show a necessary...

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$C^{*}$ -algebras, positive scalar curvature, and the Novikov conjecture

Calcul du spectre de certaines nilvariétés compactes de dimension 3

Calibrated geometries in Grassmann manifolds.

Canonical forms for separability structures with less than five Killing tensors

Canonical metric on the domain of discontinuity of a kleinian group

Certain connections between time functions and compact spacelike submanifolds

Cheeger's finiteness theorem for diffeomorphism classes of Riemannian manifolds.

Cheeger's inequality with a boundary term.

Clodes Geodesics on Non-Compact Riemannian Manifolds.

Closed Geodesics on Complete Surfaces.

Closed geodesics on surfaces of genus 0

Cohomogeneity and positive curvature in low dimensions.

Collapse of warped submersions

Collapsing and soul theorem in three-dimension

Collapsing of Riemannian manifolds and eigenvalues of La-place operator.

Collapsing Riemannian Manifolds to the Circle.

Commensurability classes and volumes of hyperbolic 3-manifolds

Compact flat manifolds with holonomy group $𝐙_{2} ⨁ 𝐙_{2}$ (II)

Compact manifolds with exceptional holonomy.

Compactification conforme des variétés asymptotiquement plates

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