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arXiv research

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3 results for “λ_1-extremality”

Riemannian

λ_1

-extremal Metrics on Generalized Flag Manifoldsmath.DG

Study finds conditions for Kähler-Einstein metrics on flag manifolds.

problem Characterizing Kähler-Einstein metrics on flag manifolds.

method Using Lie theoretic data, establish a sufficient and necessary condition for

λ_1

-extremality.

result Identifies criteria for a metric to be a critical point of the first eigenvalue functional.

Kähler-Einstein metrics flag manifolds Lie theory λ_1-extremality generalized flag manifolds

2023-11-22abs ↗pdf ↗

Rigidity of

k

-extremal submanifolds in a spheremath.DG

The paper examines rigidity of special submanifolds in spheres with curvature constraints.

problem Rigidity of

k

-extremal submanifolds in a sphere under curvature conditions.

method Proves pinching theorems for submanifolds with various curvature conditions.

result Various curvature conditions lead to rigidity of

k

-extremal submanifolds.

rigidity submanifolds sphere curvature pinching theorems

2023-05-18abs ↗pdf ↗

An extremal eigenvalue problem in Kähler geometrymath.DG

We study Laplace eigenvalues $λ_k$ on Kähler manifolds as functionals on the space of Kähler metrics with cohomologous Kähler forms. We introduce a natural notion of a $λ_k$ -extremal Kähler metric and obtain necessary and sufficient conditions for it. A particular attention is paid to the $λ_1$ -extremal properties of K…

2014-11-28abs ↗pdf ↗