TetrapodTetrapods ('tɛtrəˌpɒdz; ) are four-limbed vertebrate animals constituting the superclass Tetrapoda (tɛ'træpədə). It includes all extant and extinct amphibians, and the amniotes which in turn evolved into the sauropsids (reptiles, including dinosaurs and therefore birds) and synapsids (extinct pelycosaurs, therapsids and all extant mammals). Some tetrapods such as snakes, legless lizards and caecilians had evolved to become limbless via mutations of the Hox gene, although some do still have a pair of vestigial spurs that are remnants of the hindlimbs.
Linear complex structureIn mathematics, a complex structure on a real vector space V is an automorphism of V that squares to the minus identity, −I. Such a structure on V allows one to define multiplication by complex scalars in a canonical fashion so as to regard V as a complex vector space. Every complex vector space can be equipped with a compatible complex structure, however, there is in general no canonical such structure. Complex structures have applications in representation theory as well as in complex geometry where they play an essential role in the definition of almost complex manifolds, by contrast to complex manifolds.
Generalized complex structureIn the field of mathematics known as differential geometry, a generalized complex structure is a property of a differential manifold that includes as special cases a complex structure and a symplectic structure. Generalized complex structures were introduced by Nigel Hitchin in 2002 and further developed by his students Marco Gualtieri and Gil Cavalcanti.
VertebrateVertebrates (ˈvɜrtəbrɪts,_-ˌbreɪts) are animals with spinal cords and bony or cartilaginous backbones, including all mammals, birds, reptiles, amphibians and fish. The vertebrates consist of all the taxa within the subphylum Vertebrata (ˌvɜrtəˈbreɪtə) (chordates with backbones) and represent the overwhelming majority of the phylum Chordata, with currently about 69,963 species described.
Almost complex manifoldIn mathematics, an almost complex manifold is a smooth manifold equipped with a smooth linear complex structure on each tangent space. Every complex manifold is an almost complex manifold, but there are almost complex manifolds that are not complex manifolds. Almost complex structures have important applications in symplectic geometry. The concept is due to Charles Ehresmann and Heinz Hopf in the 1940s. Let M be a smooth manifold.
Plant evolutionary developmental biologyEvolutionary developmental biology (evo-devo) is the study of developmental programs and patterns from an evolutionary perspective. It seeks to understand the various influences shaping the form and nature of life on the planet. Evo-devo arose as a separate branch of science rather recently. An early sign of this occurred in 1999. Most of the synthesis in evo-devo has been in the field of animal evolution, one reason being the presence of model systems like Drosophila melanogaster, C. elegans, zebrafish and Xenopus laevis.
Spin structureIn differential geometry, a spin structure on an orientable Riemannian manifold (M, g) allows one to define associated spinor bundles, giving rise to the notion of a spinor in differential geometry. Spin structures have wide applications to mathematical physics, in particular to quantum field theory where they are an essential ingredient in the definition of any theory with uncharged fermions. They are also of purely mathematical interest in differential geometry, algebraic topology, and K theory.
QuadrupedalismQuadrupedalism is a form of locomotion where four limbs are used to bear weight and move around. An animal or machine that usually maintains a four-legged posture and moves using all four limbs is said to be a quadruped (from Latin quattuor for "four", and pes, pedis for "foot"). Quadruped animals are found among both vertebrates and invertebrates. Although the words ‘quadruped’ and ‘tetrapod’ are both derived from terms meaning ‘four-footed’, they have distinct meanings.
Fish finFins are distinctive anatomical features composed of bony spines or rays protruding from the body of Actinopterygii and Chondrichthyes fishes. They are covered with skin and joined together either in a webbed fashion, as seen in most bony fish, or similar to a flipper, as seen in sharks. Apart from the tail or caudal fin, fish fins have no direct connection with the spine and are supported only by muscles. Their principal function is to help the fish swim.
Hox geneHox genes, a subset of homeobox genes, are a group of related genes that specify regions of the body plan of an embryo along the head-tail axis of animals. Hox proteins encode and specify the characteristics of 'position', ensuring that the correct structures form in the correct places of the body. For example, Hox genes in insects specify which appendages form on a segment (for example, legs, antennae, and wings in fruit flies), and Hox genes in vertebrates specify the types and shape of vertebrae that will form.
