Periclimenes dardanicola chiefly white, with red along the edges of the carapace and the abdominal somites. The legs are transparent yellow, with red bands. "P. dardanicola" is associated with the sea anemone "Calliactis", which is carried by hermit crabs of the genus "Dardanus", including "Dardanus arrosor", "D. crassimanus", "D. lagopodes" and "D. pedunculatus". This is one of the few examples of ecological associations between two species of decapod crustaceans. Specimens of "Periclimenes dardanicola" have been collected from various locations in the western Pacific Ocean, namely Suruga Bay (Japan), Vietnam, and Borneo (Indonesia). Although only formally described in 2006, this species has been
History of manifolds and varieties History of manifolds and varieties The study of manifolds combines many important areas of mathematics: it generalizes concepts such as curves and surfaces as well as ideas from linear algebra and topology. Certain special classes of manifolds also have additional algebraic structure; they may behave like groups, for instance. In that case, they are called Lie Groups. Alternatively, they may be described by polynomial equations, in which case they are called algebraic varieties, and if they additionally carry a group structure, they are called algebraic groups. The term "manifold" comes from German "Mannigfaltigkeit," by Riemann. In English, "manifold" refers to