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Universal spaces for manifolds equipped with an integral closed $k$ -form

Hông-Vân Lê (2007)

Archivum Mathematicum

In this note we prove that any integral closed $k$ -form $φ^{k}$ , $k \geq 3$ , on a m-dimensional manifold $M^{m}$ , $m \geq k$ , is the restriction of a universal closed $k$ -form $h^{k}$ on a universal manifold $U^{d (m, k)}$ as a result of an embedding of $M^{m}$ to $U^{d (m, k)}$ .

Unstable minimal surfaces and Heegaard splittings.

Joel Hass, Charles Frohman (1989)

Inventiones mathematicae

Untermannigfaltigkeiten reduktiver Räume

Peter Wintgen (1975)

Czechoslovak Mathematical Journal

Untermannigfaltigkeiten von homogenen Räumen

Leo Boček (1971)

Czechoslovak Mathematical Journal

Untermannigfaltigkieten mit paralleler zweiter Fundamentalform in euklidischen Räumen und Sphären.

Rainer Walden (1973)

Manuscripta mathematica

Upper bound for the first eigenvalue of algebraic submanifolds.

S.T. Yau, J.-P. Bourguignon, P. Li (1994)

Commentarii mathematici Helvetici

Upper bounds on the length of a shortest closed geodesic and quantitative Hurewicz theorem

Alexander Nabutovsky, Regina Rotman (2003)

Journal of the European Mathematical Society

In this paper we present two upper bounds on the length of a shortest closed geodesic on compact Riemannian manifolds. The first upper bound depends on an upper bound on sectional curvature and an upper bound on the volume of the manifold. The second upper bound will be given in terms of a lower bound on sectional curvature, an upper bound on the diameter and a lower bound on the volume. The related questions that will also be studied are the following: given a contractible $k$ -dimensional sphere...