By Arvanitogeorgos, Andreas
It's outstanding that lots approximately Lie teams can be packed into this small publication. yet after interpreting it, scholars may be well-prepared to proceed with extra complex, graduate-level subject matters in differential geometry or the speculation of Lie teams.
The concept of Lie teams contains many parts of arithmetic: algebra, differential geometry, algebraic geometry, research, and differential equations. during this ebook, Arvanitoyeorgos outlines adequate of the necessities to get the reader begun. He then chooses a course via this wealthy and various idea that goals for an figuring out of the geometry of Lie teams and homogeneous areas. during this method, he avoids the additional aspect wanted for an intensive dialogue of illustration concept.
Lie teams and homogeneous areas are particularly precious to review in geometry, as they supply very good examples the place amounts (such as curvature) are more uncomplicated to compute. a very good knowing of them offers lasting instinct, particularly in differential geometry.
The writer offers numerous examples and computations. themes mentioned contain the category of compact and attached Lie teams, Lie algebras, geometrical features of compact Lie teams and reductive homogeneous areas, and critical periods of homogeneous areas, corresponding to symmetric areas and flag manifolds. purposes to extra complicated themes also are incorporated, similar to homogeneous Einstein metrics, Hamiltonian structures, and homogeneous geodesics in homogeneous areas.
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Additional resources for An Introduction to Lie Groups and the Geometry of Homogeneous Spaces [+ errata]
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