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SUMMARY:Andrés Lipa Carrizales (UFF)
DTSTART:20260619T170000Z
DTEND:20260619T180000Z
DTSTAMP:20260604T015249Z
UID:AmSurAmSulGeometry/110
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/AmSurAmSulGe
 ometry/110/">Divergence identity for the scalar curvature and rigidity of 
 Codazzi tensors</a>\nby Andrés Lipa Carrizales (UFF) as part of Geometry 
 Webinar AmSur /AmSul\n\nInteractive livestream: https://meet.google.com/nz
 d-idoy-zej\nView-only livestream: https://meet.google.com/nzd-idoy-zej\n\n
 Abstract\nIn this joint work with Xu Cheng and Detang Zhou we introduce a 
 local vector field on an $n$-dimensional Riemannian manifold\, defined as 
 the sum of the covariant derivatives of a local orthonormal frame\, and de
 rive an explicit identity for its divergence\, decomposed into a scalar cu
 rvature term and an auxiliary term involving connection coefficients. This
  result is applied to rigidity problems for Codazzi symmetric tensors. In 
 particular\, we give a new proof of a Tang-Yan theorem\, which states that
  on a closed $n$-dimensional manifold with nonnegative scalar curvature\, 
 a smooth Codazzi symmetric tensor whose trace invariants up to order $n 
 − 1$ are constant must have constant eigenvalues. We also obtain further
  rigidity results under assumptions on elementary symmetric functions of t
 he eigenvalues\, with applications to the isoparametric rigidity of closed
  hypersurfaces in the unit sphere.\n
LOCATION:https://researchseminars.org/talk/AmSurAmSulGeometry/110/
URL:https://meet.google.com/nzd-idoy-zej
URL:https://meet.google.com/nzd-idoy-zej
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