Mannheim Offsets of the Timelike Ruled Surfaces with Spacelike Rulings in Dual Lorentzian Space

TL;DR

This paper characterizes Mannheim offsets of timelike ruled surfaces with spacelike rulings in dual Lorentzian space, exploring their invariants, developability, and spherical projections to advance geometric understanding.

Contribution

It provides new characterizations and relations for Mannheim offsets of timelike ruled surfaces, including developable cases, in dual Lorentzian space.

Findings

Relations between integral invariants of Mannheim offsets

Characterization of developable Mannheim offsets

Connections between spherical projections and invariants

Abstract

In this paper, we obtain the characterizations of Mannheim offsets of the timelike ruled surface with spacelike rulings in dual Lorentzian space. We give the relations between terms of their integral invariants and also we give the new characterization of the Mannheim offsets of developable timelike ruled surface. Moreover, we obtain the relationships between the area of projections of spherical images for Mannheim offsets of timelike ruled surfaces and their integral invariants.