Closed Legendre geodesics in Sasaki manifolds

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  • Max-Planck-Institut für Mathematik in den Naturwissenschaften (MIS)
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Details

OriginalspracheEnglisch
Seiten (von - bis)23-47
Seitenumfang25
FachzeitschriftNew York journal of mathematics
Jahrgang9
PublikationsstatusVeröffentlicht - 1 Dez. 2003
Extern publiziertJa

Abstract

If L ⊂ M is a Legendre submanifold in a Sasaki manifold, then the mean curvature flow does not preserve the Legendre condition. We define a kind of mean curvature flow for Legendre submanifolds which slightly differs from the standard one and then we prove that closed Legendre curves L in a Sasaki space form M converge to closed Legendre geodesics, if k2 + σ + 3 ≤ 0 and rot(L) = 0, where σ denotes the sectional curvature of the contact plane ξ and k and rot(L) are the curvature respectively the rotation number of L. If rot(L) ≠ 0, we obtain convergence of a subsequence to Legendre curves with constant curvature. In case σ + 3 ≤ 0 and if the Legendre angle α of the initial curve satisfies osc (α) ≤ π, then we also prove convergence to a closed Legendre geodesic.

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Closed Legendre geodesics in Sasaki manifolds. / Smoczyk, Knut.
in: New York journal of mathematics, Jahrgang 9, 01.12.2003, S. 23-47.

Publikation: Beitrag in FachzeitschriftArtikelForschungPeer-Review

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