悠然
发表于 2025-3-26 23:03:01
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colloquial
发表于 2025-3-27 04:15:47
Basic Forms, Spectral Sequence, Characteristic Form,nctions.are independent of.i.e..The exterior derivative preserves basic forms, since.for w basic. Thus the set.of all basic forms constitutes a subcomplex.of the De Rham complex.We also denote.Ω.=.Its cohomology.is the basic cohomology of .. It plays the role of the De Rham cohomology of the leaf sp
令人苦恼
发表于 2025-3-27 08:13:48
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Alopecia-Areata
发表于 2025-3-27 10:12:31
Structure of Riemannian Foliations, observations. The first is that the canonical lift.of a Riemannian foliation . to the bundle. of orthonormal frames of .is a transversally parallelizable Riemannian foliation. The canonical lift. on.is a foliation of the same dimension as . on ., and invariant under the action of the orthogonal str
Airtight
发表于 2025-3-27 15:27:02
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灰姑娘
发表于 2025-3-27 19:01:48
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攀登
发表于 2025-3-27 22:44:36
Examples and Definition of Foliations, the case of a foliation of . by the level hypersurfaces of a smooth function. → ℝ. The submersion condition is the requirement of the absence of critical points for . (this is of course only possible if . is not compact).
Radiation
发表于 2025-3-28 03:01:56
1017-0480 ion of the basic concepts in the theory of foliations in the first four chapters, the subject is narrowed down to Riemannian foliations on closed manifolds beginning with Chapter 5. Following the discussion of the special case of flows in Chapter 6, Chapters 7 and 8 are de voted to Hodge theory for
intrude
发表于 2025-3-28 10:13:12
Book 1997 basic concepts in the theory of foliations in the first four chapters, the subject is narrowed down to Riemannian foliations on closed manifolds beginning with Chapter 5. Following the discussion of the special case of flows in Chapter 6, Chapters 7 and 8 are de voted to Hodge theory for the trans
向外
发表于 2025-3-28 11:12:42
Holonomy, Second Fundamental Form, Mean Curvature, space of the fibration ℝ × .ℝ →.with (.,.) ∼ (. + ., (-1) .) being the equivalence relation defining the total space. The leaves are circles, which are 2-fold coverings of the central circle . = 0, except for the central circle itself. If . = . and .:.→ . is the rotation through an angle ., then th