3-dimensional F-manifolds

F-manifolds are complex manifolds with a multiplication with unit on the holomorphic tangent bundle with a certain integrability condition. Here, the local classification of 3-dimensional F-manifolds with or without Euler fields is pursued.

Identities of the Riemannian Curvature Tensor of Almost C(ʎ)-Manifolds

The geometry of the Riemannian curvature tensor of an almost C(λ)-manifold is studied. We have obtained several identities of the Riemannian curvature tensor of almost C(λ)-manifolds. Four additional identities are distinguished from these identities, on the basis of which four classes of almost C(λ)-manifolds are determined. A local classification of each of the distinguished classes of almost C(λ)-manifolds is obtained. It is proved that the set of almost C(λ)-manifolds of class R_1 coincides with the set of almost C(λ)-manifolds of class R_2, and it is also proved that the set of almost C(λ)-manifolds of class R_3 coincides with the set of almost C(λ)- manifolds of class R_4. We have found that an almost C(λ)-manifold, dimension greater than 3, is a manifold of class R_4 if and only if it is a cosymplectic manifold, i.e. when it is locally equivalent to the product of the Kähler manifold and the real line.

Mapping Rice Paddy Based on Machine Learning with Sentinel-2 Multi-Temporal Data: Model Comparison and Transferability

Rice is an important agricultural crop in the Southwest Hilly Area, China, but there has been a lack of efficient and accurate monitoring methods in the region. Recently, convolutional neural networks (CNNs) have obtained considerable achievements in the remote sensing community. However, it has not been widely used in mapping a rice paddy, and most studies lack the comparison of classification effectiveness and efficiency between CNNs and other classic machine learning models and their transferability. This study aims to develop various machine learning classification models with remote sensing data for comparing the local accuracy of classifiers and evaluating the transferability of pretrained classifiers. Therefore, two types of experiments were designed: local classification experiments and model transferability experiments. These experiments were conducted using cloud-free Sentinel-2 multi-temporal data in Banan District and Zhongxian County, typical hilly areas of Southwestern China. A pure pixel extraction algorithm was designed based on land-use vector data and a Google Earth Online image. Four convolutional neural network (CNN) algorithms (one-dimensional (Conv-1D), two-dimensional (Conv-2D) and three-dimensional (Conv-3D_1 and Conv-3D_2) convolutional neural networks) were developed and compared with four widely used classifiers (random forest (RF), extreme gradient boosting (XGBoost), support vector machine (SVM) and multilayer perceptron (MLP)). Recall, precision, overall accuracy (OA) and F1 score were applied to evaluate classification accuracy. The results showed that Conv-2D performed best in local classification experiments with OA of 93.14% and F1 score of 0.8552 in Banan District, OA of 92.53% and F1 score of 0.8399 in Zhongxian County. CNN-based models except Conv-1D provided more desirable performance than non-CNN classifiers. Besides, among the non-CNN classifiers, XGBoost received the best result with OA of 89.73% and F1 score of 0.7742 in Banan District, SVM received the best result with OA of 88.57% and F1 score of 0.7538 in Zhongxian County. In model transferability experiments, almost all CNN classifiers had low transferability. RF and XGBoost models have achieved acceptable F1 scores for transfer (RF = 0.6673 and 0.6469, XGBoost = 0.7171 and 0.6709, respectively).