On the Geometry of Conullity Two Manifolds
On the Geometry of Conullity Two Manifolds
상세정보
- 자료유형
- 학위논문 서양
- 최종처리일시
- 20250211151114
- ISBN
- 9798382830407
- DDC
- 510
- 서명/저자
- On the Geometry of Conullity Two Manifolds
- 발행사항
- [Sl] : University of Pennsylvania, 2024
- 발행사항
- Ann Arbor : ProQuest Dissertations & Theses, 2024
- 형태사항
- 65 p
- 주기사항
- Source: Dissertations Abstracts International, Volume: 85-12, Section: B.
- 주기사항
- Advisor: Ziller, Wolfgang.
- 학위논문주기
- Thesis (Ph.D.)--University of Pennsylvania, 2024.
- 초록/해제
- 요약We investigate the structure of complete locally irreducible conullity two Riemannian manifolds. If Γ is the nullity space of the curvature tensor of a complete manifold Mn and both n and dim Γ are constant then Γ is completely integrable with flat leaves. Utilizing tools such as the splitting tensor we arrive at a natural classification of two potential cases: the so-called nilpotent conullity two manifolds whose splitting tensors are nilpotent, and the hyperbolic conullity two manifolds whose splitting tensors have complex conjugate non-real eigenvalues. In the nilpotent case we arrive at a Lipschitz foliation by totally geodesic flat hyperplanes and determine the metric on an open dense subset in terms of n − 1 functions. We also find examples where the foliation is only smooth on specific subsets, and we determine that the fundamental group must either be trivial or infinite cyclic. In the hyperbolic case we make some observations that could lead to the development of a classification.
- 일반주제명
- Mathematics
- 일반주제명
- Applied mathematics
- 키워드
- Curvature tensor
- 키워드
- Hyperbolic case
- 키워드
- Nilpotent case
- 기타저자
- University of Pennsylvania Mathematics
- 기본자료저록
- Dissertations Abstracts International. 85-12B.
- 전자적 위치 및 접속
- 로그인 후 원문을 볼 수 있습니다.
MARC
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■020 ▼a9798382830407
■035 ▼a(MiAaPQ)AAI31145145
■040 ▼aMiAaPQ▼cMiAaPQ
■0820 ▼a510
■1001 ▼aVan Hook, Jacob Arthur.
■24510▼aOn the Geometry of Conullity Two Manifolds
■260 ▼a[Sl]▼bUniversity of Pennsylvania▼c2024
■260 1▼aAnn Arbor▼bProQuest Dissertations & Theses▼c2024
■300 ▼a65 p
■500 ▼aSource: Dissertations Abstracts International, Volume: 85-12, Section: B.
■500 ▼aAdvisor: Ziller, Wolfgang.
■5021 ▼aThesis (Ph.D.)--University of Pennsylvania, 2024.
■520 ▼aWe investigate the structure of complete locally irreducible conullity two Riemannian manifolds. If Γ is the nullity space of the curvature tensor of a complete manifold Mn and both n and dim Γ are constant then Γ is completely integrable with flat leaves. Utilizing tools such as the splitting tensor we arrive at a natural classification of two potential cases: the so-called nilpotent conullity two manifolds whose splitting tensors are nilpotent, and the hyperbolic conullity two manifolds whose splitting tensors have complex conjugate non-real eigenvalues. In the nilpotent case we arrive at a Lipschitz foliation by totally geodesic flat hyperplanes and determine the metric on an open dense subset in terms of n − 1 functions. We also find examples where the foliation is only smooth on specific subsets, and we determine that the fundamental group must either be trivial or infinite cyclic. In the hyperbolic case we make some observations that could lead to the development of a classification.
■590 ▼aSchool code: 0175.
■650 4▼aMathematics
■650 4▼aApplied mathematics
■653 ▼aCurvature tensor
■653 ▼aGeodesic flat hyperplanes
■653 ▼aHyperbolic case
■653 ▼aNilpotent case
■653 ▼aHyperbolic conullity
■690 ▼a0405
■690 ▼a0364
■71020▼aUniversity of Pennsylvania▼bMathematics.
■7730 ▼tDissertations Abstracts International▼g85-12B.
■790 ▼a0175
■791 ▼aPh.D.
■792 ▼a2024
■793 ▼aEnglish
■85640▼uhttp://www.riss.kr/pdu/ddodLink.do?id=T17160772▼nKERIS▼z이 자료의 원문은 한국교육학술정보원에서 제공합니다.
