Let $p:X \rightarrow B$ be a covering map. Is it true that if $X$ admits hyperbolic metric then $B$ admits hyperbolic metric?
2026-04-01 18:59:50.1775069990
True of False? If covering space admits hyperbolic metric then base space admits hyperbolic metric.
55 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail At
1
There are 1 best solutions below
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 ALGEBRAIC-TOPOLOGY
- How to compute homology group of $S^1 \times S^n$
- the degree of a map from $S^2$ to $S^2$
- Show $f$ and $g$ are both homeomorphism mapping of $T^2$ but $f$ is not homotopy equivalent with $g.$
- Chain homotopy on linear chains: confusion from Hatcher's book
- Compute Thom and Euler class
- Are these cycles boundaries?
- a problem related with path lifting property
- Bott and Tu exercise 6.5 - Reducing the structure group of a vector bundle to $O(n)$
- Cohomology groups of a torus minus a finite number of disjoint open disks
- CW-structure on $S^n$ and orientations
Related Questions in METRIC-SPACES
- Show that $d:\mathbb{C}\times\mathbb{C}\rightarrow[0,\infty[$ is a metric on $\mathbb{C}$.
- Question on minimizing the infimum distance of a point from a non compact set
- Is hedgehog of countable spininess separable space?
- Lemma 1.8.2 - Convex Bodies: The Brunn-Minkowski Theory
- Closure and Subsets of Normed Vector Spaces
- Is the following set open/closed/compact in the metric space?
- Triangle inequality for metric space where the metric is angles between vectors
- continuous surjective function from $n$-sphere to unit interval
- Show that $f$ with $f(\overline{x})=0$ is continuous for every $\overline{x}\in[0,1]$.
- Help in understanding proof of Heine-Borel Theorem from Simmons
Related Questions in HYPERBOLIC-GEOMETRY
- Sharing endpoint at infinity
- CAT(0) references request
- Do the loops "Snakes" by M.C. Escher correspond to a regular tilling of the hyperbolic plane?
- How to find the Fuschian group associated with a region of the complex plane
- Hyperbolic circles in the hyperbolic model
- Area of an hyperbolic triangle made by two geodesic and an horocycle
- Concavity of distance to the boundary in Riemannian manifolds
- Differential Equation of Circles orthogonal to a fixed Circle
- Is there a volume formula for hyperbolic tetrahedron
- Can you generalize the Triangle group to other polygons?
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?
False. Consider the covering of the torus $\mathbb{T}^2$ by the plane $\mathbb{R}^2$. You can put a metric of constant curvature $-1$ on $\mathbb{R}^2$ by identifying it with any model of the hyperbolic plane but any metric on $\mathbb{T}^2$ must be either flat or have points of positive, zero and negative curvature.