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In differential geometry, a one-form (or covector field) on a differentiable manifold is a differential form of degree one, that is, a smooth section of the cotangent bundle. [1] Equivalently, a one-form on a manifold is a smooth mapping of the total space of the tangent bundle of to whose restriction to each fibre is a linear functional on the ...
Geomorphology (from Ancient Greek γῆ (gê) 'earth' μορφή (morphḗ) 'form' and λόγος 'study') [2] is the scientific study of the origin and evolution of topographic and bathymetric features generated by physical, chemical or biological processes operating at or near Earth's surface.
Solidified lava flow in Hawaii Sedimentary layers in Badlands National Park, South Dakota Metamorphic rock, Nunavut, Canada. Geology (from Ancient Greek γῆ (gê) 'earth' and λoγία () 'study of, discourse') [1] [2] is a branch of natural science concerned with the Earth and other astronomical objects, the rocks of which they are composed, and the processes by which they change over time. [3]
A geological survey is the systematic investigation of the geology beneath a given piece of ground for the purpose of creating a geological map or model.Geological surveying employs techniques from the traditional walk-over survey, studying outcrops and landforms, to intrusive methods, such as hand augering and machine-driven boreholes, to the use of geophysical techniques and remote sensing ...
Geography (from Ancient Greek γεωγραφία geōgraphía; combining gê 'Earth' and gráphō 'write', literally 'Earth writing') is the study of the lands, features, inhabitants, and phenomena of Earth.
Foundations of Differential Geometry is an influential 2-volume mathematics book on differential geometry written by Shoshichi Kobayashi and Katsumi Nomizu. The first volume was published in 1963 and the second in 1969, by Interscience Publishers. Both were published again in 1996 as Wiley Classics Library.
The three teams for the 2025 NBA All-Star Game were selected Thursday night on TNT by the "Inside the NBA" crew of Shaquille O'Neal, Kenny Smith and Charles Barkley.
A local 1-form on M is a contact form if the restriction of its exterior derivative to H is a non-degenerate two-form and thus induces a symplectic structure on H p at each point. If the distribution H can be defined by a global one-form α {\displaystyle \alpha } then this form is contact if and only if the top-dimensional form