sectional curvature वाक्य
उदाहरण वाक्य
मोबाइल
- *PM : sectional curvature determines Riemann curvature tensor, id = 7924 new !-- WP guess : sectional curvature determines Riemann curvature tensor-- Status:
- A consequence of this formula is that the sectional curvature satisfies 1 \ leq K ( \ sigma ) \ leq 4 for all 2-planes \ sigma.
- The standard counterexample is complex projective space with the Fubini Study metric; sectional curvatures of this metric take on values between 1 and 4, with endpoints included.
- Ricci curvature and more specifically those with negative sectional curvature . ( A strange and interesting fact is that all closed three-manifolds admit metrics with negative Ricci curvatures!
- This system is useful in physics, especially in the physical quantities are identified with geometric quantities such as areas, lengths, dimensionless numbers, path curvatures, or sectional curvatures.
- In particular, the four-dimensional manifold " S " 2 & times; " S " 2 should admit no Riemannian metric with positive sectional curvature.
- :Suppose is complete, connected and non-compact with sectional curvature, and there exists a point in where the sectional curvature ( in all sectional directions ) is strictly positive.
- :Suppose is complete, connected and non-compact with sectional curvature, and there exists a point in where the sectional curvature ( in all sectional directions ) is strictly positive.
- For example, Gromov and Lawson showed that a closed manifold that admits a metric with sectional curvature d " 0, such as a torus, has no metric with positive scalar curvature.
- Another consequence of the Geometrisation conjecture is that any closed 3-manifold which admits a Riemannian metric with negative sectional curvatures admits in fact a Riemannian metric with constant sectional curvature-1.
- Another consequence of the Geometrisation conjecture is that any closed 3-manifold which admits a Riemannian metric with negative sectional curvatures admits in fact a Riemannian metric with constant sectional curvature-1.
- Let M _ i be a sequence of n dimensional Riemannian manifolds, where \ sec ( M _ i ) denotes the sectional curvature of the " i " th manifold.
- In two dimensions sectional curvature is always pointwise constant since there is only one two-dimensional subspace \ Pi _ p \ subset T _ p M, namely T _ p M.
- The 2 theorem states : a Dehn filling of " M " with each filling slope greater than 2 results in a 3-manifold with a complete metric of negative sectional curvature.
- Moreover, if the diameter is equal to ? / " " k ", then the manifold is isometric to a sphere of a constant sectional curvature " k ".
- If for each point in a connected Riemannian manifold ( of dimension three or greater ) the sectional curvature is independent of the tangent 2-plane, then the sectional curvature is in fact constant on the whole manifold.
- If for each point in a connected Riemannian manifold ( of dimension three or greater ) the sectional curvature is independent of the tangent 2-plane, then the sectional curvature is in fact constant on the whole manifold.
- On the other hand one can fix the bound of sectional curvature and get the diameter going to zero, so the almost-flat manifold is a special case of a collapsing manifold, which is collapsing along all directions.
- If tighter bounds on the sectional curvature are known, then this property generalizes to give a comparison theorem between geodesic triangles in " M " and those in a suitable simply connected space form; see Toponogov's theorem.
- Indeed, if \ xi is a vector of unit length on a Riemannian " n "-manifold, then is precisely times the average value of the sectional curvature, taken over all the 2-planes containing \ xi.
sectional curvature sentences in Hindi. What are the example sentences for sectional curvature? sectional curvature English meaning, translation, pronunciation, synonyms and example sentences are provided by Hindlish.com.