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On timelike Bonnet surfaces in Lorentzian 3-manifold

Athoumane Niang, Ameth Ndiaye, Adama Thiandoum

Abstract

In this paper we generalized a result of Soley Ersoy and Kemal Eren [10] about Bonnet timelike surface in Minkowski 3-space. We give a necessary and sufficient condition for a surface M in a Lorentzian 3-space to be timelike Bonnet surface. At the end, a theorem of classification of timelike Bonnet surface in a Lorentzian 3-space is given.

On timelike Bonnet surfaces in Lorentzian 3-manifold

Abstract

In this paper we generalized a result of Soley Ersoy and Kemal Eren [10] about Bonnet timelike surface in Minkowski 3-space. We give a necessary and sufficient condition for a surface M in a Lorentzian 3-space to be timelike Bonnet surface. At the end, a theorem of classification of timelike Bonnet surface in a Lorentzian 3-space is given.
Paper Structure (3 sections, 2 theorems, 50 equations)

This paper contains 3 sections, 2 theorems, 50 equations.

Table of Contents

  1. Introduction
  2. Some basic formulas
  3. Timelike Bonnet surface in $\mathbb{L}^3$

Key Result

Theorem 3.3

Let $M$ be timelike surface in $\mathbb{L}^3$ of constant mean curvature $H$ with $H^2>K$. If $M$ has zero normal curvature then $M$ has one parameter family of non trivial isometric deformations preserving the mean curvature; that is $M$ is timelike Bonnet surface in $\mathbb{L}^3$.

Theorems & Definitions (4)

  • Remark 3.1
  • Remark 3.2
  • Theorem 3.3
  • Theorem 3.4