negative curvature sentence in Hindi
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- Every complete, connected, simply-connected manifold of constant negative curvature " 1 is isometric to the real hyperbolic space \ mathbb { H } ^ n.
- The image like an expanding horn on the right shows a universe with negative curvature in time, and no finite end, no boundary in the upward time dimension.
- When M is of negative curvature and \ varepsilon is smaller than the Margulis constant for \ widetilde M the structure of the components of the thin part is very simple.
- One species has a Type II functional response-which occurs when individuals must spend time handling handling resources before moving on to the next resource-and has negative curvature.
- In geometry, methods of ergodic theory have been used to study the geodesic flow on Riemannian manifolds, starting with the results of Eberhard Hopf for Riemann surfaces of negative curvature.
- In 1898 Jacques Hadamard published an influential study of the chaotic motion of a free particle gliding frictionlessly on a surface of constant negative curvature, called " Hadamard's billiards ".
- Conversely, adding a diamond-shaped "'gusset "'produces negative curvature at its tips and positive curvature at its middle ( useful in designing stuffed animals ).
- He proposed that harmonic maps be used to prove rigidity of the complex structure for K�hler manifolds with strongly negative curvature, a program that was successfully carried out by Yum-Tong Siu.
- General relativity merely adds a connection between the spatial curvature of the universe and the energy of such a particle : positive total energy implies negative curvature and negative total energy implies positive curvature.
- Showed that a complete immersed surface in "'R "'3 cannot have constant negative curvature, and show that the curvature cannot be bounded above by a negative constant.
- Each cluster is about 6 nanometers wide and consists of about 4000 carbon atoms linked in graphite-like sheets that are given negative curvature by the inclusion of heptagons among the regular hexagonal pattern.
- The Kodaira dimension divides all " n "-dimensional varieties into " n " + 2 classes, which ( very roughly ) go from positive curvature to negative curvature.
- Subtracting a diamond-shaped dart produces positive curvature at the outer points of the diamond, and negative curvature at the middle points that are brought together ( good for the bust or back ).
- The sum of the angles of a triangle on a surface of positive curvature will exceed ?, while the sum of the angles of a triangle on a surface of negative curvature will be less than ?.
- The attractive force of gravity created by matter is due to a negative curvature of spacetime, represented in the rubber sheet analogy by the negatively curved ( trumpet-bell-like ) dip in the sheet.
- The system considers the motion of a free ( frictionless ) particle on a surface of constant negative curvature, the simplest compact Riemann surface, which is the surface of genus two : a donut with two holes.
- Geometrically, there is a very rough correspondence between Kodaira dimension and curvature : negative Kodaira dimension corresponds to positive curvature, zero Kodaira dimension corresponds to flatness, and maximum Kodaira dimension ( general type ) corresponds to negative curvature.
- In a 1993 paper Bowditch proved that five standard characterisations of geometric finiteness for discrete groups of isometries of Hadamard manifold of pinched ( but not necessarily constant ) negative curvature and of arbitrary dimension " n " e " 2.
- Agol's proof relies on the use of manifolds of pinched negative curvature and on Canary's trick of " diskbusting " that allows to replace a compressible end with an incompressible end, for which the conjecture has already been proved.
- Alternatively, the condition of negative curvature at a maximum is also equivalent to stating that the following logarithmic derivatives of the geometric means " G X " and " G ( 1 " X ) " are positive, since:
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