3 papers
math.DG2021
New Hsiung-Minkowski identities
R. Albuquerque
We find the first three most general Minkowski or Hsiung-Minkowski identities relating the total mean curvatures , of degrees , of a closed hypersurface immersed…
math.DG2021
The Euler characteristic of hypersurfaces in space forms and applications to isoparametric hypersurfaces
R. Albuquerque
We revisit Allendoerfer-Weil's formula for the Euler characteristic of embedded hypersurfaces in constant sectional curvature manifolds, first taking some time to re-prove it while…
math.DG2018
Notes on the Sasaki metric
Rui Albuquerque
We survey on the geometry of the tangent bundle of a Riemannian manifold, endowed with the classical metric established by S. Sasaki 60 years ago. Following the results of Sasaki,…