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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...

Collapsed Riemannian Manifolds with Bounded Diameter and Bounded Covering Geometry.

J. Cheeger, X. Rong (1995)

Geometric and functional analysis

Collapsing and soul theorem in three-dimension

Tatao Yamaguchi (1996/1997)

Séminaire de théorie spectrale et géométrie

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

K. Fukaya (1987)

Inventiones mathematicae

Collapsing Riemannian Manifolds to the Circle.

Xiao-Wie Peng (1989)

Mathematische Zeitschrift

Collars in PSL $(2, 𝐇)$ .

Kellerhals, Ruth (2001)

Annales Academiae Scientiarum Fennicae. Mathematica

Collective geodesic flows

Léo T. Butler, Gabriel P. Paternain (2003)

Annales de l’institut Fourier

We show that most compact semi-simple Lie groups carry many left invariant metrics with positive topological entropy. We also show that many homogeneous spaces admit collective Riemannian metrics arbitrarily close to the bi-invariant metric and whose geodesic flow has positive topological entropy. Other properties of collective geodesic flows are also discussed.

Combinatorial differential geometry and ideal Bianchi–Ricci identities II – the torsion case

Josef Janyška, Martin Markl (2012)

Archivum Mathematicum

This paper is a continuation of [2], dealing with a general, not-necessarily torsion-free, connection. It characterizes all possible systems of generators for vector-field valued operators that depend naturally on a set of vector fields and a linear connection, describes the size of the space of such operators and proves the existence of an ‘ideal’ basis consisting of operators with given leading terms which satisfy the (generalized) Bianchi–Ricci identities without corrections.

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Cohomologies et déformations de certaines algèbres de Lie $ℤ$ -graduées

Cohomology and connection on $S 1$ -bundles

Cohomology of biquotients.

Cohomology of Compact Hyperkähler Manifolds and its Applications.

Cohomology of CR-submanifolds

Cohomology of Symplectomorphism Groups and Critical Values of Hamiltonians.

Coincidence set of minimal surfaces for the thin obstacle.

Coisotropic bundles and induced representations

Coisotropic varieties and their generating families

Collapse of warped submersions