A note on parallel mean curvature surfaces and Codazzi operators

Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Global Riemannian geometry, including pinching (53C20)

Cites Work

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Simons type equation in \(\mathbb S^{2}\times \mathbb R\) and \(\mathbb H^{2}\times \mathbb R\) and applications
A classification theorem for complete PMC surfaces with non-negative Gaussian curvature in \(M^n(c) \times \mathbb{R}\)
Complete constant mean curvature surfaces in homogeneous spaces
A Hopf differential for constant mean curvature surfaces in \(\mathbb S^2 \times \mathbb R\) and \(\mathbb H^2 \times\mathbb R\)
A note on surfaces with parallel mean curvature
Surfaces with parallel mean curvature vector in complex space forms
Complete constant mean curvature surfaces and Bernstein type theorems in \(\mathbb M^2 \times \mathbb R\)
A Hopf theorem for ambient spaces of dimensions higher than three
The Codazzi equation for surfaces
Efimov's theorem in dimension greater than two
Abstract Weingarten surfaces
Hypersurfaces with constant scalar curvature
Constant mean curvature surfaces in \({\mathbb {M}}^2(c)\times \mathbb {R}\) and finite total curvature
Surfaces of constant mean curvature in manifolds of constant curvature
Surfaces with parallel mean curvature in \(S^{3}\times \mathbb R\) and \(H^{3}\times \mathbb R\)
Complete surfaces with non-positive extrinsic curvature in \(\mathbb{H}^3\) and \(\mathbb{S}^3\)
Complete surfaces in \(E^ 3\) with constant mean curvature
Efimov's theorem about complete immersed surfaces of negative curvature
Differential equations on riemannian manifolds and their geometric applications
The Abresch–Rosenberg shape operator and applications

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