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Obata’s Rigidity Theorem for Metric Measure Spaces

100%

Ketterer C.

Analysis and Geometry in Metric Spaces

2015

tom 3

nr 1

We prove Obata’s rigidity theorem for metric measure spaces that satisfy a Riemannian curvaturedimension condition. Additionally,we show that a lower bound K for the generalizedHessian of a sufficiently regular function u holds if and only if u is K-convex. A corollary is also a rigidity result for higher order eigenvalues.

The *-holonomy group of the Stefan suspension of a diffeomorphism

100%

Piątkowski A.

Annales Polonici Mathematici

1993

tom 58

nr 2

123-129

The definition of a Stefan suspension of a diffeomorphism is given. If $𝓖_g$ is the Stefan suspension of the diffeomorphism g over a Stefan foliation 𝓖, and G₀ ∈ 𝓖 satisfies the condition $g|G₀ = id_{G₀}$, then we compute the *-holonomy group for the leaf $F₀ ∈ 𝓖_g$ determined by G₀. A representative element of the *-holonomy along the standard imbedding of S¹ into F₀ is characterized. A corollary for the case when G₀ contains only one point is derived.

Ograniczanie wyników

1 Analysis and Geometry in Metric Spaces

1 Annales Polonici Mathematici

1 Ketterer C.

1 Piątkowski A.

1 2015

1 1993

Wyniki wyszukiwania

Obata’s Rigidity Theorem for Metric Measure Spaces

The *-holonomy group of the Stefan suspension of a diffeomorphism