On Interpolating Sesqui-Harmonic Maps Between Riemannian Manifolds.

Area of Science:

• Differential Geometry
• Mathematical Physics
• Geometric Analysis

Background:

• Harmonic and biharmonic maps are fundamental concepts in geometric analysis.
• Existing functionals for harmonic and biharmonic maps lack a unified interpolation framework.
• The action functional for bosonic strings with extrinsic curvature provides motivation.

Purpose of the Study:

• Introduce a novel action functional for maps between Riemannian manifolds.
• Define and investigate interpolating sesqui-harmonic maps as critical points of this new functional.
• Initiate a rigorous mathematical treatment of the functional and its critical points.

Main Methods:

• Construction of an action functional interpolating between harmonic and biharmonic map actions.
• Definition of interpolating sesqui-harmonic maps.
• Development of a rigorous mathematical framework for analysis.
• Study of basic properties of critical points.

Main Results:

• A new action functional is proposed for maps between Riemannian manifolds.
• The concept of interpolating sesqui-harmonic maps is formally introduced.
• Initial mathematical analysis of the functional and its critical points is presented.

Conclusions:

• The introduced functional provides a bridge between harmonic and biharmonic map theories.
• Interpolating sesqui-harmonic maps represent a new class of geometric objects.
• Further research into the properties and applications of these maps is warranted.