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Novel theorems for the cotangent bundle endowed with metallic structures on a differentiable manifold
Mohammad Nazrul Islam Khan1, Nahid Fatima2
1Department of Computer Engineering, College of Computer, Qassim University, Buraydah 51452, Saudi Arabia.
Heliyon
|July 1, 2024
Summary
This study explores metallic structures and their lifts within the cotangent bundle. Researchers established integrability conditions for metallic structures using differential equations.
Area of Science:
- Differential Geometry
- Mathematical Physics
Background:
- Metallic structures are fundamental in differential geometry.
- The cotangent bundle is a key space in mathematical physics.
Purpose of the Study:
- To investigate complete, horizontal, and diagonal lifts of metallic structures.
- To compute the Nijenhuis tensor for metallic structures.
- To determine integrability conditions.
Main Methods:
- Calculus of variations
- Differential geometry techniques
- Partial differential equations
Main Results:
- Characterization of complete, horizontal, and diagonal lifts.
- Computation of the Nijenhuis tensor for metallic structures.
- Establishment of integrability conditions.
Conclusions:
- The study provides a comprehensive analysis of metallic structures in the cotangent bundle.
- Integrability conditions were successfully derived, offering insights into the behavior of these structures.
Keywords:
53C1558A30Complete liftDiagonal liftDifferential equationsHorizontal liftIntegrabilityMetallic structureNijenhuis tensorPartial differential equationsMore Related Videos
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