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The Frölicher-Nijenhuis bracket and its applications in geometry and calculus of variations
Šramková, Kristína ; Tomáš, Jiří (referee) ; Kureš, Miroslav (advisor)
This Master's thesis clarifies the significance of Frölicher-Nijenhuis bracket and its applications in problems of physics. The basic apparatus for these applications is differential geometry on manifolds, tensor calculus and differential forms, which are contained in the first part of the thesis. The second part summarizes the basic theory of calculus of variations on manifolds and its selected applications in the field of physics. The last part of the thesis is devoted to the applications of Frölicher-Nijenhuis bracket in the derivation of Maxwell's equations and to the description of the geometry of ordinary differential equations.
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Tensors and their applications
Korbel, Filip ; Tomáš, Jiří (referee) ; Doupovec, Miroslav (advisor)
The goal of this thesis is to provide an overview of basic terms and results of tensor calculus. We introduce tensors as multilinear mappings and introduce basic tensor operations. In the next section, we give some examples of tensors, especially from the field of differential geometry.
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The Frölicher-Nijenhuis bracket and its applications in geometry and calculus of variations
Šramková, Kristína ; Tomáš, Jiří (referee) ; Kureš, Miroslav (advisor)
This Master's thesis clarifies the significance of Frölicher-Nijenhuis bracket and its applications in problems of physics. The basic apparatus for these applications is differential geometry on manifolds, tensor calculus and differential forms, which are contained in the first part of the thesis. The second part summarizes the basic theory of calculus of variations on manifolds and its selected applications in the field of physics. The last part of the thesis is devoted to the applications of Frölicher-Nijenhuis bracket in the derivation of Maxwell's equations and to the description of the geometry of ordinary differential equations.
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Tensors and their applications
Korbel, Filip ; Tomáš, Jiří (referee) ; Doupovec, Miroslav (advisor)
The goal of this thesis is to provide an overview of basic terms and results of tensor calculus. We introduce tensors as multilinear mappings and introduce basic tensor operations. In the next section, we give some examples of tensors, especially from the field of differential geometry.
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