Local Wintgen ideal submanifolds
Marcos Dajczer, Theodoros Vlachos
TL;DR
This paper classifies Wintgen ideal submanifolds in space forms, which are characterized by equality in the DDVV inequality, providing a detailed local parametric description.
Contribution
It offers the first comprehensive local parametric classification of Wintgen ideal submanifolds in space forms.
Findings
Classification results for Wintgen ideal submanifolds
Explicit local parametrizations derived
Conditions for equality in the DDVV inequality established
Abstract
This paper is dedicated to the local parametric classification of Wintgen ideal submanifolds in space forms. These submanifolds are characterized by the pointwise attainment of equality in the DDVV inequality, which relates the scalar curvature, the length of the mean curvature vector field and the normal curvature tensor.
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