| Full text | |
| Author(s): |
de Lima, R. F.
;
Manfio, F.
;
dos Santos, J. P.
Total Authors: 3
|
| Document type: | Journal article |
| Source: | Results in Mathematics; v. 77, n. 6, p. 26-pg., 2022-12-01. |
| Abstract | |
We consider Einstein hypersurfaces of warped products Ix(omega)Q(epsilon)(n), where I subset of R is an open interval and Q(epsilon)(n) is the simply connected space form of dimension n >= 2 and constant sectional curvature c epsilon. {-1, 0, 1}. We show that, for all c epsilon R (resp. c > 0), there exist rotational hypersurfaces of constant sectional curvature c in I x (omega) Hn and I x (omega) Rn (resp. I x (omega) S-n), provided that omega is nonconstant. We also show that the gradient T of the height function of any Einstein hypersurface of I x (omega)Q(epsilon)(n) (if nonzero) is one of its principal directions. Then, we consider a particular type of Einstein hypersurface of I x (omega)Q(epsilon)(n) with non vanishing T-which we call ideal-and prove that, for n > 3, such a hypersurface Sigma has either precisely two or precisely three distinct principal curvatures everywhere. We show that, in the latter case, there exist such a Sigma for certain warping functions omega whereas in the former case S is necessarily of constant sectional curvature and rotational, regardless the warping function.. We also characterize ideal Einstein hypersurfaces of I x (omega) Q(epsilon)(n) with no vanishing angle function as local graphs on families of isoparametric hypersurfaces of Q(epsilon)(n) (AU) | |
| FAPESP's process: | 16/23746-6 - Algebraic, topological and analytical techniques in differential geometry and geometric analysis |
| Grantee: | Paolo Piccione |
| Support Opportunities: | Research Projects - Thematic Grants |