A note on parallel mean curvature surfaces and Codazzi operators
Felippe Guimar\~aes
TL;DR
This paper explores the properties of surfaces with parallel mean curvature using Codazzi operators and investigates their characteristics in product spaces with non-positive Gaussian curvature.
Contribution
It introduces an intrinsic theorem for surfaces via Codazzi operators and applies Simons' formula to analyze surfaces with parallel mean curvature in specific spaces.
Findings
Established an intrinsic Klotz-Osserman type theorem for surfaces.
Analyzed surfaces with parallel mean curvature in product spaces.
Provided conditions for surfaces with non-positive Gaussian curvature.
Abstract
We present an intrinsic Klotz-Osserman type theorem for surfaces in terms of Codazzi operators. Additionally, utilizing Simons' formula, we investigate surfaces with parallel mean curvature with non-positive Gaussian curvature in product spaces.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Point processes and geometric inequalities · Geometry and complex manifolds