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Differential geometry of the Fermat ...

Hadnot, Jason.

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Differential geometry of the Fermat quartic surface.

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Differential geometry of the Fermat quartic surface./
作者:	Hadnot, Jason.
面頁冊數:	126 p.
附註:	Source: Dissertation Abstracts International, Volume: 74-07(E), Section: B.
Contained By:	Dissertation Abstracts International74-07B(E).
標題:	Mathematics. -
電子資源:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3536963
ISBN:	9781267959379

Differential geometry of the Fermat quartic surface.
Hadnot, Jason.

Differential geometry of the Fermat quartic surface. - 126 p.

Source: Dissertation Abstracts International, Volume: 74-07(E), Section: B.

Thesis (Ph.D.)--Boston University, 2013.

We examine the differential geometry of the Fermat Quartic surface X40+X43-X4 1-X42 = 0 in CP3 with induced Fubini-Study metric. We show that the differential equations of geodesics, when restricted to the real Fermat quartic surface inside the full complex quartic, can be reduced to two non-linear differential equations with rational coefficients along especially chosen geodesics. This simplification opens up the possibility of parametrizing these geodesics in terms of genus three Abelian integrals and their inversions. Furthermore the identity component of the differential Galois group of normal variational equation, derived from the geodesic equation along one of these selected curves, is SL(2, C ). By Morales-Ramis theory the Hamiltonian system defining the geodesic equations is not integrable in a neighborhood of this solution by meromorphic integrals.

ISBN: 9781267959379Subjects--Topical Terms:

515831
Mathematics.

Differential geometry of the Fermat quartic surface.
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520 $a We examine the differential geometry of the Fermat Quartic surface X40+X43-X4 1-X42 = 0 in CP3 with induced Fubini-Study metric. We show that the differential equations of geodesics, when restricted to the real Fermat quartic surface inside the full complex quartic, can be reduced to two non-linear differential equations with rational coefficients along especially chosen geodesics. This simplification opens up the possibility of parametrizing these geodesics in terms of genus three Abelian integrals and their inversions. Furthermore the identity component of the differential Galois group of normal variational equation, derived from the geodesic equation along one of these selected curves, is SL(2, C ). By Morales-Ramis theory the Hamiltonian system defining the geodesic equations is not integrable in a neighborhood of this solution by meromorphic integrals.
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