Develops the theory of jet single-time Lagrange geometry and
presents modern-day applications
"Jet Single-Time Lagrange Geometry and Its Applications" guides
readers through the advantages of jet single-time Lagrange geometry
for geometrical modeling. With comprehensive chapters that outline
topics ranging in complexity from basic to advanced, the book
explores current and emerging applications across a broad range of
fields, including mathematics, theoretical and atmospheric physics,
economics, and theoretical biology.
The authors begin by presenting basic theoretical concepts that
serve as the foundation for understanding how and why the discussed
theory works. Subusequent chapters compare the geometrical and
physical aspects of jet relativistic time-dependent Lagrange
geometry to the classical time-dependent Lagrange geometry. A
collection of jet geometrical objects are also examined such as
d-tensors, relativistic time-dependent semisprays, harmonic curves,
and nonlinear connections. Numerous applications, including the
gravitational theory developed by both the Berwald-Moor metric and
the Chernov metric, are also presented.
Throughout the book, the authors offer numerous examples that
illustrate how the theory is put into practice, and they also
present numerous applications in which the solutions of first-order
ordinary differential equation systems are regarded as harmonic
curves on 1-jet spaces. In addition, numerous opportunities are
provided for readers to gain skill in applying jet single-time
Lagrange geometry to solve a wide range of problems.
Extensively classroom-tested to ensure an accessible
presentation, "Jet Single-Time Lagrange Geometry and Its
Applications" is an excellent book for courses on differential
geometry, relativity theory, and mathematical models at the
graduate level. The book also serves as an excellent reference for
researchers, professionals, and academics in physics, biology,
mathematics, and economics who would like to learn more about
model-providing geometric structures.
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