On Submanifolds with constant Möbius Ricci curvature
Abstract
In the Möbius geometry of submanifolds there exists an important Möbius invariant tensor called the Möbius metric which together with the Möbius second fundamental form, the Blaschke tensor and the Möbius form constitute a complete system of conformal invariants for umbilic-free submanifolds when the dimension n ≥ 3. An umbilic-free immersion f:Mn→ ℝm is said to have constant Möbius Ricci curvature if its Möbius metric has constant Ricci curvature. In this paper, we classify umbilic-free immersions f:Mn→ ℝm with constant Möbius Ricci curvature, flat normal bundle and two distinct principal normal vector fields. We prove that a submanifold with constant Möbius Ricci curvature and flat normal bundle has closed Möbius form, and then we classify such submanifolds provided the Möbius form vanishes identically on Mn.
Related
- Sharp scalar and Ricci curvature pinching theorems for Lagrangian submanifolds in the homogeneous nearly Kähler Six-sphere
- Biharmonic Wintgen ideal submanifolds in Riemannian manifolds of constant sectional curvature
- Legendrian submanifolds in the unit sphere with conformal Maslov form and constant sectional curvature
- Four-dimensional pseudo-umbilical biharmonic submanifolds in six-dimensional Riemannian manifolds of constant sectional curvature
- Submanifolds of higher rank with curvature normals of constant length
BibTeX
@misc{antas2026submanifolds,
title = {{On Submanifolds with constant Möbius Ricci curvature}},
author = {M. S. R. Antas},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.07152},
eprint = {2611.07152},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.07152},
}
RIS
TY - UNPB
TI - On Submanifolds with constant Möbius Ricci curvature
AU - M. S. R. Antas
PY - 2026
DA - 2026/11/04
PB - arXiv
DO - 10.48550/arxiv.2611.07152
UR - https://arxiv.org/abs/2611.07152
AB - In the Möbius geometry of submanifolds there exists an important Möbius invariant tensor called the Möbius metric which together with the Möbius second fundamental form, the Blaschke tensor and the Möbius form constitute a complete system of conformal invariants for umbilic-free submanifolds when the dimension n ≥ 3. An umbilic-free immersion f:M^n→ ℝ^m is said to have constant Möbius Ricci curvature if its Möbius metric has constant Ricci curvature. In this paper, we classify umbilic-free immersions f:M^n→ ℝ^m with constant Möbius Ricci curvature, flat normal bundle and two distinct principal normal vector fields. We prove that a submanifold with constant Möbius Ricci curvature and flat normal bundle has closed Möbius form, and then we classify such submanifolds provided the Möbius form vanishes identically on M^n.
ER -