I wish to learn about holonomy groups of Riemannian manifolds and the Ambrose- Singer theorem. Please advise some references other than the original paper of Ambrose and Singer.
2026-03-26 02:51:16.1774493476
Ambrose Singer Theorem
1k Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail At
1
There are 1 best solutions below
Related Questions in REFERENCE-REQUEST
- Best book to study Lie group theory
- Alternative definition for characteristic foliation of a surface
- Transition from theory of PDEs to applied analysis and industrial problems and models with PDEs
- Random variables in integrals, how to analyze?
- Abstract Algebra Preparation
- Definition of matrix valued smooth function
- CLT for Martingales
- Almost locality of cubic spline interpolation
- Identify sequences from OEIS or the literature, or find examples of odd integers $n\geq 1$ satisfying these equations related to odd perfect numbers
- property of Lebesgue measure involving small intervals
Related Questions in DIFFERENTIAL-GEOMETRY
- Smooth Principal Bundle from continuous transition functions?
- Compute Thom and Euler class
- Holonomy bundle is a covering space
- Alternative definition for characteristic foliation of a surface
- Studying regular space curves when restricted to two differentiable functions
- What kind of curvature does a cylinder have?
- A new type of curvature multivector for surfaces?
- Regular surfaces with boundary and $C^1$ domains
- Show that two isometries induce the same linear mapping
- geodesic of infinite length without self-intersections
Related Questions in RIEMANNIAN-GEOMETRY
- What is the correct formula for the Ricci curvature of a warped manifold?
- How to show that extension of linear connection commutes with contraction.
- geodesic of infinite length without self-intersections
- Levi-Civita-connection of an embedded submanifold is induced by the orthogonal projection of the Levi-Civita-connection of the original manifold
- Geodesically convex neighborhoods
- The induced Riemannian metric is not smooth on the diagonal
- Intrinsic vs. Extrinsic notions of Harmonic maps.
- Equivalence of different "balls" in Riemannian manifold.
- Why is the index of a harmonic map finite?
- A closed manifold of negative Ricci curvature has no conformal vector fields
Related Questions in HOLONOMY
- Holonomy group and irreducible $\mathrm{SU}(2)$-connections
- In what way can the Riemannian curvature be regarded as a two-form with values in $\mathfrak{hol}$?
- Is the determinant of the holonomy gauge invariant / significant?
- Recovering a principal connection from its monodromy
- Holonomy and curvature on a surface
- Is the comparator $U(y,x)$ in Gauge Theory the same as a holonomy?
- Translation Holonomy
- Combinatorial analog of holonomy on a planar graph with quadrilateral faces
- Is there a class of non-symmetric spaces $G/SO(n)$ such that $Hol(G/SO(n))=SO(n)$?
- Correspondence between flat connections and fundamental group representations
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Find $E[XY|Y+Z=1 ]$
- Refuting the Anti-Cantor Cranks
- What are imaginary numbers?
- Determine the adjoint of $\tilde Q(x)$ for $\tilde Q(x)u:=(Qu)(x)$ where $Q:U→L^2(Ω,ℝ^d$ is a Hilbert-Schmidt operator and $U$ is a Hilbert space
- Why does this innovative method of subtraction from a third grader always work?
- How do we know that the number $1$ is not equal to the number $-1$?
- What are the Implications of having VΩ as a model for a theory?
- Defining a Galois Field based on primitive element versus polynomial?
- Can't find the relationship between two columns of numbers. Please Help
- Is computer science a branch of mathematics?
- Is there a bijection of $\mathbb{R}^n$ with itself such that the forward map is connected but the inverse is not?
- Identification of a quadrilateral as a trapezoid, rectangle, or square
- Generator of inertia group in function field extension
Popular # Hahtags
second-order-logic
numerical-methods
puzzle
logic
probability
number-theory
winding-number
real-analysis
integration
calculus
complex-analysis
sequences-and-series
proof-writing
set-theory
functions
homotopy-theory
elementary-number-theory
ordinary-differential-equations
circles
derivatives
game-theory
definite-integrals
elementary-set-theory
limits
multivariable-calculus
geometry
algebraic-number-theory
proof-verification
partial-derivative
algebra-precalculus
Popular Questions
- What is the integral of 1/x?
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- Is a matrix multiplied with its transpose something special?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- How to tell if a set of vectors spans a space?
- Calculus question taking derivative to find horizontal tangent line
- How to determine if a function is one-to-one?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- Is this Batman equation for real?
- How to find perpendicular vector to another vector?
- How to find mean and median from histogram
- How many sides does a circle have?
References as follows
HLAVATÝ, VÁCLAV. “The Holonomy Group I. The Curvature Tensor.” Journal of Mathematics and Mechanics, vol. 8, no. 2, 1959, pp. 285–307. JSTOR, http://www.jstor.org/stable/24900561 . Accessed 22 Aug. 2022.
The above is the first of six papers on ‘The Holonomy Group’, by V.Hlavaty, that are all available on JSTOR. Individuals may be able to sign up for a free account with JSTOR.
I suggest starting with a first brief look at pg. 12 of the second paper of the six, see (4.1).
HLAVATÝ, V. “The Holonomy Group II. The Lie Group Induced by a Tensor.” Journal of Mathematics and Mechanics, vol. 8, no. 4, 1959, pp. 597–622. JSTOR, http://www.jstor.org/stable/24900677. Accessed 22 Aug. 2022.
HLAVATÝ, VÁCLAV. “The Holonomy Group III. Metrisable Spaces.” Journal of Mathematics and Mechanics, vol. 9, no. 1, 1960, pp. 89–122. JSTOR, http://www.jstor.org/stable/24900513. Accessed 22 Aug. 2022.
HLAVATÝ, VÁCLAV. “The Holonomy Group IV. The General Ln with Symmetric Connection.” Journal of Mathematics and Mechanics, vol. 9, no. 3, 1960, pp. 453–96. JSTOR, http://www.jstor.org/stable/24900484. Accessed 22 Aug. 2022.
HLAVATÝ, VÁCLAV. “The Holonomy Group V. Weyl Space W 4 , First Part.” Journal of Mathematics and Mechanics, vol. 10, no. 2, 1961, pp. 317–48. JSTOR, http://www.jstor.org/stable/24900828. Accessed 22 Aug. 2022.
HLAVATÝ, V. “The Holonomy Group VI. Weyl Space W 4 , Second Part.” Journal of Mathematics and Mechanics, vol. 11, no. 1, 1962, pp. 35–59. JSTOR, http://www.jstor.org/stable/24900845. Accessed 22 Aug. 2022.