Abstract
AbstractIn this paper, we locally classify the surfaces immersed into the non-flat (Riemannian or Lorentzian) 3-space forms satisfying the condition $$\Box \vec {\textbf{H}}=\lambda \vec {\textbf{H}}$$
□
H
→
=
λ
H
→
for a real number $$\lambda $$
λ
, where $$\vec {\textbf{H}}$$
H
→
is the mean curvature vector field and $$\Box $$
□
denotes the Cheng–Yau operator of the surface. We obtain the classification result by proving, at a first step, that the mean curvature function must be constant and, in a second step, we complete the classification.
Funder
Ministerio de Ciencia e Innovación
Fundación Séneca
Universidad Nacional de Colombia
Publisher
Springer Science and Business Media LLC