Pseudo-Riemannian Submanifolds with 3-Planar Geodesics
Kadri Arslan, Bet\"ul Bulca, G\"unay \"Ozt\"urk
TL;DR
This paper investigates pseudo-Riemannian submanifolds with 3-planar geodesic normal sections, focusing on W-curves (helices), and establishes conditions for normal sections to be W-curves.
Contribution
It provides necessary and sufficient conditions for normal sections to be W-curves on pseudo-Riemannian submanifolds, advancing understanding of their geometric properties.
Findings
Characterization of 3-planar geodesic normal sections
Conditions for normal sections to be W-curves
Enhanced understanding of pseudo-Riemannian submanifold geometry
Abstract
In the present paper we study pseudo-Riemannian submanifolds which have 3-planar geodesic normal sections.We consider W-curves (helices) on pseudo-Riemannian submanifolds. Finally, we give neccessary and sufficient condition for a normal section to be a W-curve on pseudo-Riemannian submanifolds.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Advanced Differential Geometry Research · Geometry and complex manifolds