In the mathematical field of differential geometry, the Levi-Civita parallelogramoid is a quadrilateral[1] in a curved space whose construction generalizes that of a parallelogram in the Euclidean plane. It is named for its discoverer, Tullio Levi-Civita. Like a parallelogram, two opposite sides AA′ and BB′ of a parallelogramoid are parallel (via parallel transport along side AB) and the same length as each other, but the fourth side A′B′ will not in general be parallel to or the same length as the side AB, although it will be straight (a geodesic).[2]
- ^ Levi-Civita, Tullio (1917), "Nozione di parallelismo in una varietà qualunque e conseguente specificazione geometrica della curvatura riemanniana" [Notion of parallelism in any variety and consequent geometric specification of the Riemannian curvature], Rendiconti del Circolo Matematico di Palermo (in Italian), 42: 199.
- ^ In the article by Levi-Civita (1917, p. 199), the segments AB and A'B ′ are called (respectively) the base and suprabase of the parallelogramoid in question.