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Kramer, W.

doi:10.1023/a:1006644823883

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2005

2024

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Cited by 4 publications

(1 citation statement)

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“…Min-Oo discussed the extremality/rigidity of hermitian symmetric spaces of compact type in [12]. The extremality/rigidity of complex and quaternionic projective spaces was established by Kramer [8]. Later, Goette and Semmelmann [4] proved that compact symmetric spaces of type G/K with rk(G) − rk(K) ≤ 1 are extremal (see also [3]).…”

Section: Introductionmentioning

confidence: 99%

Gromov Rigidity of Bi-Invariant Metrics on Lie Groups and Homogeneous Spaces

Sun

Dai

2020

SIGMA

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Gromov asked if the bi-invariant metrics on a compact Lie group are extremal compared to any other metrics. In this note, we prove that the bi-invariant metrics on a compact connected semi-simple Lie group G are extremal (in fact rigid) in the sense of Gromov when compared to the left-invariant metrics. In fact the same result holds for a compact connected homogeneous manifold G/H with G compact connect and semi-simple.

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Section: Introductionmentioning

confidence: 99%

Gromov Rigidity of Bi-Invariant Metrics on Lie Groups and Homogeneous Spaces

Sun

Dai

2020

SIGMA

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Extremality for the Vafa–Witten bound on the sphere

Herzlich

2005

GAFA, Geom. funct. anal.

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Spectral constant rigidity of warped product metrics

Chai,

Pyo,

Wan

2024

Journal of London Math Soc

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A theorem of Llarull says that if a smooth metric on the ‐sphere is bounded below by the standard round metric and the scalar curvature of is bounded below by , then the metric must be the standard round metric. We prove a spectral Llarull theorem by replacing the bound by a lower bound on the first eigenvalue of an elliptic operator involving the Laplacian and the scalar curvature . We utilize two methods: spinor and spacetime harmonic function.

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Cited by 4 publications

References 6 publications

Gromov Rigidity of Bi-Invariant Metrics on Lie Groups and Homogeneous Spaces

Gromov Rigidity of Bi-Invariant Metrics on Lie Groups and Homogeneous Spaces

Extremality for the Vafa–Witten bound on the sphere

Spectral constant rigidity of warped product metrics

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