Hermit crab shells instead, as shown by a specimen of "Palaeopagurus vandenengeli" from the Speeton Clay, Yorkshire, UK from the Lower Cretaceous. Hermit crab Hermit crabs are decapod crustaceans of the superfamily Paguroidea. Most of the approximately 1,110 species possess an asymmetrical abdomen that is concealed in a scavenged mollusc shell carried around by the hermit crab. Most species have long, spirally curved abdomens, which are soft, unlike the hard, calcified abdomens seen in related crustaceans. The vulnerable abdomen is protected from predators by a salvaged empty seashell carried by the hermit crab, into which its whole body can retract. Most frequently,
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