Work

On the existence of a minimal time-like surface of the Minkowski space with constant curvature of its Grassmann image

Year: 2024

Type: article

Abstract: We investigate the curvature of the Grassmann manifold along planes tangent to the Grassmann image of two-dimensional time-like minimal surfaces in four-dimensional Minkowski space. We establish the existence of two-dimensional time-like minimal surfaces whose Grassmann images exhibit constant curvature K=1. Furthermore, we demonstrate that no time-like minimal surfaces exist with a non-degenerate Grassmann image of constant curvature K≠1.

Source: Proceedings of the International Geometry Center

DOI: 10.15673/pigc.v17i3.2879

Authors: Maryna Hrechnieva, Polina Stiehantseva

Institution: Zaporizhzhia National University

Language: English

Topic: Advanced Differential Geometry Research

Subfield: Astronomy and Astrophysics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: diamond

OpenAlex ID: W4405725131

FWCI:

Cites: 12

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Related to: 10