user: Please answer this: Information:  - In mathematics, the tangent space of a manifold facilitates the generalization of vectors from affine spaces to general manifolds, since in the latter case one cannot simply subtract two points to obtain a vector that gives the displacement of the one point from the other.  - In mathematics, especially in set theory, a set "A" is a subset of a set "B", or equivalently "B" is a superset of "A", if "A" is "contained" inside "B", that is, all elements of "A" are also elements of "B". "A" and "B" may coincide. The relationship of one set being a subset of another is called inclusion or sometimes containment.  - In differential geometry, a (smooth) Riemannian manifold or (smooth) Riemannian space ("M","g") is a real smooth manifold "M" equipped with an inner product formula_1 on the tangent space formula_2 at each point formula_3 that varies smoothly from point to point in the sense that if "X" and "Y" are vector fields on "M", then formula_4 is a smooth function. The family formula_1 of inner products is called a Riemannian metric (tensor). These terms are named after the German mathematician Bernhard Riemann. The study of Riemannian manifolds constitutes the subject called Riemannian geometry.  - Differential geometry is a mathematical discipline that uses the techniques of differential calculus, integral calculus, linear algebra and multilinear algebra to study problems in geometry. The theory of plane and space curves and surfaces in the three-dimensional Euclidean space formed the basis for development of differential geometry during the 18th century and the 19th century.   - Georg Friedrich Bernhard Riemann (17 September 1826  20 July 1866) was a German mathematician who made contributions to analysis, number theory, and differential geometry. In the field of real analysis, he is mostly known for the first rigorous formulation of the integral, the Riemann integral, and his work on Fourier series. His contributions to complex analysis include most notably the introduction of Riemann surfaces, breaking new ground in a natural, geometric treatment of complex analysis. His famous 1859 paper on the prime-counting function, containing the original statement of the Riemann hypothesis, is regarded, although it is his only paper in the field, as one of the most influential papers in analytic number theory. Through his pioneering contributions to differential geometry, Riemann laid the foundations of the mathematics of general relativity.  - Riemannian geometry is the branch of differential geometry that studies Riemannian manifolds, smooth manifolds with a "Riemannian metric", i.e. with an inner product on the tangent space at each point that varies smoothly from point to point. This gives, in particular, local notions of angle, length of curves, surface area and volume. From those, some other global quantities can be derived by integrating local contributions.  - In mathematics, a submanifold of a manifold "M" is a subset "S" which itself has the structure of a manifold, and for which the inclusion map "S"  "M" satisfies certain properties. There are different types of submanifolds depending on exactly which properties are required. Different authors often have different definitions.  - In mathematics, a manifold is a topological space that locally resembles Euclidean space near each point. More precisely, each point of an "n"-dimensional manifold has a neighbourhood that is homeomorphic to the Euclidean space of dimension "n".  - A Riemannian submanifold N of a Riemannian manifold M is a submanifold of M equipped with the Riemannian metric inherited from M. The image of an isometric immersion is a Riemannian submanifold .  - In vector calculus, a vector field is an assignment of a vector to each point in a subset of space. A vector field in the plane (for instance), can be visualised as: a collection of arrows with a given magnitude and direction, each attached to a point in the plane. Vector fields are often used to model, for example, the speed and direction of a moving fluid throughout space, or the strength and direction of some force, such as the magnetic or gravitational force, as it changes from point to point.  - In mathematics, if formula_1 is a subset of formula_2, then the inclusion map (also inclusion function, insertion, or canonical injection) is the function formula_3 that sends each element, formula_4, of formula_1 to formula_4, treated as an element of formula_2:  - Mathematics (from Greek  "máthma", knowledge, study, learning) is the study of topics such as quantity (numbers), structure, space, and change. There is a range of views among mathematicians and philosophers as to the exact scope and definition of mathematics.    What entity does 'riemannian submanifold' has the relation 'named after' with?
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Answer: bernhard riemann


Please answer this: Information:  - FTSE Group is a British provider of stock market indices and associated data services, wholly owned by the London Stock Exchange (LSE) and operating out of premises in Canary Wharf. It operates the well known UK FTSE 100 Index as well as a number of other indices. FTSE stands for Financial Times Stock Exchange.  - Jardine Strategic Holdings Limited ( BSX : JSHBD.BH , LSE : JDS , SGX : J37 ) is a large company that holds stock . It is a part of Jardine Matheson Holdings Limited , or Jardine 's . Jardine Strategic was a constituent of the Straits Times Index . The holding company holds substantial amounts of Dairy Farm , a convenience store group , Hongkong Land , a property group , Mandarin Oriental , a hotel group , and Jardine Cycle & Carriage , an auto group . It also owns part of the stock of the Jardine Matheson group itself . It in effect owns its own corporate parent , enabling the Keswick family to control the group without providing a majority of the capital . This expertise in protecting family owners was shared in 2005 when it took a 20 % stake in Rothschild Continuation Holdings , a major merchant bank . Jardine Strategic , as an office , is a corporate entity entrusted with managing and owning stock , in its stock portfolios . The paperwork , taxes , computer file maintenance , day - to - day share trading and security oversight of the stocks owned by this company , including that of its parent , are the purview of this company .  - The FTSE Straits Times Index (STI) is a capitalisation-weighted stock market index that is regarded as the benchmark index for the Singapore stock market. It tracks the performance of the top 30 companies listed on the Singapore Exchange. It is jointly calculated by Singapore Press Holdings (SPH), Singapore Exchange (SGX) and FTSE Group (FTSE).  - Singapore Exchange Limited (SGX) is an investment holding company located in Singapore and provides different services related to securities and derivatives trading and others. SGX is a member of the World Federation of Exchanges and the Asian and Oceanian Stock Exchanges Federation.    What entity does 'jardine strategic holdings' has the relation 'stock exchange' with?
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Answer:

assistant: london stock exchange